Module For Mathematics

JRBT 2014 COT – MUST 1st
Sem 2014 EDU 52
ALGEBRAIC EXPRESSIONS AND POLYNOMIALS
Algebra has a language of its own. That language – composed of arithmetic numbers, letters, called
variables, and other symbols- will enable you to translate verbal ideas into a universal language of
algebraic expressions. Such expressions, which can either be phrases or sentences, show important
relations between quantities and often hold the key to the solution of problems. Herein lies the true
power of algebra, and the world owes much of what it is today to the magic formulas that made
possible many modern inventions and technological advancement in science, business, and industry.
I. Objective
At the end of this instructional module, the students are expected to
1. Acquire satisfactory skill in performing the four fundamental operations with polynomials
2. Utilize this skill in manipulating polynomial in
a. Simplifying algebraic expressions
b. Evaluating algebraic expressions
c. Solving simple algebraic problems.
3. Develop perseverance in reaching one’s goals
II. PRE TEST
This is a recall of concepts and skills which you will need in this module. Answer the questions
to the best of your ability.
1. Give the property involve in each of the following open sentences.
a. a + b = b+ a d. a + (-a) = 0
b. a • (1/a) = 1 e. (a + b) + c = a + (b + c)
c. a ( b + c) = a (b) + a (c)
2. What will the sign of the result in each of the following operations?
a. (-) + (-) = ? d. (-) + (-) = ?
b. (-) (-) + ? e. (-) + (+) + ?
c. (-) (+) = ? f. (-) (-) (-) = ?

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3. Perform the indicated operations.
a. (-18) + (-25) h. 20 – (-8)
b. (20) + (-12) i. 16 + (-9) – (-15)
c. (-15) + 9 j. Subtract -3 from 0
d. -19 + 16 – 8 + 5 – 12 k. (-8) (-9)
e. 13 -21 l. (1/2) (0)
f. -15 – 9B (-20) m. (2/3) (-8) (-6)
g. -17 -14 n. (0.8) (-2) (-20)(-2)
4. Identify each of the following expressions as a numerical phrase, a numerical sentence, an
open sentence, an open phrase, or an open sentence.
a. 3x e. 4 + 5 = 3 x 3
b. 6 + 5 x 2 f. s – 7 = 8
c. 9 x 5 = 54 g. 3x – 2 = 7
d. y < 4
5. ________ and ______ are two kinds of mathematical operations
6. ________ is a numerical for a definite number
7. ________ is a statement of relationship between two numerical phrases.
8. ________ is a statement of relationship between two mathematical phrases, at least one of
which is an open phrase.

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III. ALGEBRAIC EXPRESSIONS
The following diagram should help you picture the universal set of mathematical expressions and
its subsets- the arithmetical or numerical expressions on one hand and the algebraic expressions on
the other.
U = Mathematical Expressions
Key
Arithmetical Expressions
4 + 8 ; 9 x t – 6
Numerical Phrases
Numerical Sentences
Equations
3 + 5 = 4 + 2
4 – 3 = 5 - 4
Inequalities
5 + 6 ≠ 2 x 3
-8 < 0
Algebraic Expressions
Open Phrases
Polynomial
Expression
4y - y
Polynomials
X; 4 + y
Open Sentences
Equations
2n – 8 = 6
4a + 5a = 9a
Inequalities
a ≥ 3
y – 2 ≤ 8
Key Concept
 An algebraic expression is any combination of numbers, letters and symbols which is
taken as a whole represents a number.
 Two subjects of algebraic expressions are open phrases and open sentences

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IV. EQUIVALENT EXPRESSIONS
You know that 2/4 and 6/12 are equivalent fractions because they are only different names for the
fraction ½. Similarly, algebraic expressions may also be equivalent.
Consider two pairs of expressions:
a. 5a + 3a is equivalent to 8a.
b. 7x – x is equivalent to 6x.
Proof: a. If a equals 4, then
5a + 3a = 5(4) + 3(4) 8 a = 8(4)
= 20 + 12 = 32
= 32
b. If x is replaced by 5, then
7x – x = 7(5) – 5 6x = 6(5)
= 35 – 5 = 32
= 30
V. SIMPLIFYING ALGEBRAIC EXPRESSIONS
It is very easy to find the value of any given algebraic expression if it is in its simplest form. Consider
the given expressions and their simplest form.
Given Expression Simplified form
1. y + 12y 1. 13y
2. (2x) (3y) (4y) 2. 24xy2
3. 2x + 2 = 12 3. 2x = 10 or x = 5
The process of simplifying an algebraic expression is called simplification.
Key Concept
 Two algebraic expressions having the same value for the same replacement of the
variable are said to equivalent expressions
Key Concept
 Simplification is the process of arriving at an equivalent expression which is
simpler than the original or given expression.

Sem 2014 EDU 52
VI. EVALUATING ALGEBRAIC EXPRESSIONS
Any algebraic expression is useless until one determines its values or the number it represents.
The process of finding the value of an algebraic expression is called evaluation, or evaluating an
algebraic expression. There are at least two steps in evaluating an algebraic expression. Figure out
those steps after studying the examples.
Example
1. 3x when x = (1/3)
3x = 3 (1/3) By replacement
x = 1 By multiplication
2. x + y + z when x = 6, y is -10, and x is 4
x + y + z = 6 + (-10) + 4 Why?
= (6 + 4) + (-10) Addition
= 10 + (-10) Addition
= 0 Additive Inverse
3. 4xyz when x = 5, y = 2, and x = -3
4xyz = 4(5) (2) (-3)
= -120
4. 3a + 5b + (-2c) when a = 5, b = 2, and c = 3.
3a + 5b -2c = 3•5 + 5•2 - 2•3
= 15 + 10 – 6
= 19
`
Key Concept
 The first step in evaluating an algebraic expression is substitution. It is the
process of replacing the variable by its given value.
 The second step is performing the indicated operations to obtain a single
numerical value
Key Concept
 In performing a series of operations, multiplication and division must always
be performed in the order indicated before addition and subtraction are
performed in the order or occurrence.

Sem 2014 EDU 52
VII. SYMBOLS OF GROUPING
To avoid ambiguity in expressions like 7 + 3, we make use of grouping symbols which will explicitly
give the order in which operations are to be performed. The most common symbol for grouping is
the parenthesis ( ). The brackets, [ ], braces { } and vinculum ( as in a – b – c = 25) are other
forms of parenthesis. In general, the parenthesis mean that the expression within them is to be
treated as one number. Hence, any operation indicated before the parentheses applies to the
whole expression within it. Thus, if we were to use the parentheses in evaluating 7 + 3 – 2, the
value will depend on the grouping to be made. Therefore, if one wants to add 7 to the product of 3
and 2, the expression will be (7 + 3)▪ = 20. If one wants to add 7 to the product of 3 and 2, the
expression should be 7 + (3•2) = 13. When two or more parentheses are used, one within another,
they would be removed one pair at a time starting from the innermost.
Example: [ 2d – (3-d) + 1 ] = [ 2d – 3 + d +1 ]
= 3d - 2
VIII. FORMULAS
The most useful algebraic expression is perhaps the open sentence which shows a unique
relationship between quantities and which states a rule. This rule expressed in symbols is called a
formula. Formulas are widely used in science and in business and as such are the most important
type of literal equations. Because of their usefulness, you should be able to express a statement as
a formula and, given a formula, state it in words. Finally, you should know how to evaluate a given
formula.
Some commonly used formulas
1. ⁰C = 5/9 ( ⁰F - 32) Changing temperature from ⁰Fahrenheit to
⁰Celsius
2. S = n/2 (a+1) The sum of an arithmetic series
3. W1/w2 = l1/l2 Connecting weight on a balance with length of
arms
4. V = 4/3 π r2
Volume of Sphere
5. I = prt Simple Interest
6. D = rt Distance traveled
7. A = π r2
Area of circle
8. C = 2 π r Circumference of a circle
9. I = a + (n-1) d The nth term of an arithmetic sequence
10. P = a + b + c The perimeter of a scalene triangle
11. A = H (b + b)
2
The area of a trapezoid
12. P = BR Percentage
13. R = P/B Rate or percentage
14. B = P/R The base in percentage
15. 𝑥 =
−𝑏±√𝑏2−4𝑎𝑐
2𝑎
Solving for quadratic equation

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A formula can be expressed from a verbal statement of relationship using suitable letters to
represent quantities involved. To illustrate,
Example 1:
Open Sentence: The number of days in a given number of weeks equals seven
times the number of weeks.
Formula: d = 7w, where d stands for days and w weeks.
Example 2:
Rule: The area of a triangle is equal to one-half the product of the base times the
height.
Formula: A = (1/2) bh
Formulas can be made from related numbers in a table or from a flow chart. A flow chart is much
like a formula because it tells how to go from input numbers to output numbers. Observe how a
formula can be made from a chart.
Example 1.
Flow chart for scoring or grading test. The output is the subject of the formula.
If n is the number of problems answered incorrectly, then s is the score.
If a student answered four problems incorrectly, then S = 100 – 5(4)
= 100 – 20
= 80
Start
n
MULTIPLY BY
SUBTRACT THE PRODUCT FROM 100
S
END Formula: S = 100 – 5n

Sem 2014 EDU 52
Example 2:
Flow chart for finding gain of profit
A table of values may also be used to express the relationship between two quantities and to
suggest the formula for such a relationship. Consider the following tables.
Example 1:
x 0 1 2 3 4 ? 12 20 33
y 3 4 5 6 ? 8 ? ? ?
Formula: y = x + 3
Example 2:
A Fiera runs 40km per hour. Can you give the number of kilometers it can run in the given
number of hours? If d is the number of kilometers run or the distance covered, can you give the
formula for finding d?
Hours 1 2 3 4 5 9 12 x
Distance in km 40 80 120 ? ? ? ? ?
Formula: d = 40h
START
s
SUBTRACT
g
END
Formula: g = s - c

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IX. POLYNOMIALS IN ONE VARIABLE
Mathematical expressions called polynomials play a great role in the application of mathematics to
technology and science. The modern concept of polynomials varies slightly from its traditional
definition but the two can be reconciled.
The table below is a study in contrast. It is designed to convey to you the meaning of polynomials
by presenting expressions which are polynomials and which are not. After a close scrutiny of the
table, try to frame a definition for a polynomial.
A B
These are polynomials:
1. 3; x, x2
2. x – 5; x2
+ 3x; x2
+ 2x – 4
3x + x – ⅟2 x + 5
3. xyz; 3x; 0.75x
4. -15; -x
These are nonpolynomials:
1. x + x; 6 + 5; (x+3) (x + 2)
1 – (3 + 5); - (-5)
2. √x
3. X-2
4. ⅟x
5. X-3
All polynomials are algebraic expression, though not all algebraic expressions are polynomials.
Some are polynomial expression. Now perhaps we can consider another chart that will help you
farther recognize polynomials and distinguish them from polynomial expression.
Polynomials Polynomial Expressions
1. 6; x2
2. x + 8; x – 3; x2
+ 3x – 8
3. 3x; abc; 6xyz
4. -10x
1. 2x + x; 6 + 9
2. 6x – x; x – (3x + x)
3. 4(x+2)
4. – (5x)
Key Concept
 A polynomial is a mathematical phrase, which may be real number or a
variable or the result of performing addition, subtraction, multiplication or
taking the opposite of real numbers and variables.

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A polynomial of the form x, 3x, cde, -15, and 3 is called a monomial. A monomial is either a real
number, a variable, or a product of variables or of real numbers and one or more variables. Is a
monomial a polynomial? Yes. Are all polynomials monomial? No. It is only a class of polynomials
since polynomials may be classified according to the number of terms they contain as.
1. Monomial as in x, x2
, abc
2. Binomial as in x + 2; 5x + 6
3. Trinomial as in x – 3x + 2; a + b + c
4. Quartic as in x3
– 4x2
– 5x - 1; a – b – c – d
Polynomials may also be classified according to degree. The degree of a polynomial in one variable
is determined by the greatest exponent of the variable in polynomial. As to degree, a polynomial
may be classified as
1. Constant polynomial 3. quadratic
2. Linear polynomial 4. Cubic
A polynomial like 11 may be considered as a constant polynomial in which the degree of the
variable is zero since 11 can be expressed as 11x which is equivalent to 11(1) or just 11.
A linear polynomial is one in which the highest exponents of the variable is one. Hence, 3x –
1 is a linear polynomial.
A polynomial of degree 2 like x2
– x – 6 is called quadratic.
A polynomial of degree 3 like y3
+ y2
is a cubic.
The monomial with the highest degree of the variable is called the leading monomial; its coefficient
is the leading coefficient. It is customary to write a polynomial in a standard form, i.e, the leading
monomial is written first, followed by the monomial of the next degree till you come to the lowest
degree which is usually the constant. Thus:
Not Standard Standard form
12 + x2
– x + 5x3
13 + y3
+ x – 2y2
5x3
– 2x2
+ x + 12
Y3
– 2y2
+ y + 13
Key Concept
 A monomial is a polynomial of one term. A monomial like 3 or -15 is a constant
monomial
 A binomial is a polynomial of two terms.
 A trinomial is a polynomial composed of three terms.
 A quartic is a polynomial composed of four terms or monomial

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Analyzing the expression x2
+ 3x + 5 according to the terms just defined, we say:
a. This is a trinomial in standard form.
b. It is a quadratic trinomial since it is in the second degree
c. The leading monomial is x2
d. The leading coefficient is 1
X. ADDITION OF POLYNOMIALS
Simplification of algebraic expressions requires skill in performing operations involving
polynomials. In the succeeding sections you should gain skill in those operations starting with
addition.
Quantities to be added or subtracted must always be in the same unit. Fraction can be added only
when they are similar. Likewise, only similar monomials may be added or subtracted.
A. The following sets of monomials are unlike.
1. { - 9y, -9x, 8x} 4. (3xy, 8y2
, 5x2
, y2
)
2. [5x, x2
, 2x3
] 5. (7x, 7x3
,. 8x2
)
3. (2a, 2b, -2c)
B. The following sets of monomials are similar.
1. X, 5x, -10x 4. 2xy, xy, 8xy
2. -7y, 8y, 15y 5. a2
b, -3a2
b, 10a2
b
Addition of monomials is simply a process of combining like terms to get a simple equivalent
expression. The principle is the same as adding 5 bananas to 4 bananas to get 9 bananas. Now, if
instead of bananas we have b’s then 5b + 4b gives 9b. By using the basic properties of numbers and
the rules of addition of integers which you reviewed in the first chapter, then you can solve any
addition problem similar to the sample problems.
Example :
Adding horizontally, 4b + 5b given
= (4 + 5)b DPMA
= 9b By addition
Key Concept
 Similar terms are terms or monomials which have the same literal coefficient

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Check: if b = 3, then 4b + 5b = 4(3) + 5(3)
= 12 + 15
= 27
Example 2:
12a + 7b + 15a + (-5b) Given
= (12a + 15a) + [ 7b + (-5b) ] CPA and APA
= 27a + 2b By Addition
Terms may also be added vertically following the same principle that you were taught about
arranging your addends in proper time
Example: In arithmetic In Algebra
4 (units) 4u
+ 5 (units) 5u
9 (units) 9u
Example 2: to add 53 and 24 and 2 To add 5t + 3u + 2t + 4u + 2u
5 (units) + 3 (units) 5t + 3u
+ 2 (tens) + 4 (units) 2t + 4u
+ 2 (units) + 2u
7 (tens) + 9 (units) = 79 7t + 9u
Example 3: Find the sum of 3x and 5y. The sum is only indicated as 3x + 5y. In algebra the sum of
unlike terms can only be indicated. Time, we have 7t + 9u and 3x + 5y. In algebra the sum of unlike
terms can only be indicated. Thus, we have 7t + 9u and 3x + 5y as sums.
If you know how to add monomials, then there is no reason why you can’t add multinomials. Note
how the addition of multinomials is done.
Example : Find the sum of the following trinomials: 3a + 2b -c ; 3c – 7a – 2b; and b – 5c + 5a
3a + 2b – c
-7a -2b +3c
8a + b – 5c
4a + b – 3c
However u can have any value and
the value of the 9u will depend on it.

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XI. SUBTRACTION OF POLYNOMIALS
To subtract a number from another, add the opposite of the subtrahend to the minuend. In short,
to subtract a number from another, add its additive inverse to the adder.
The same definition holds for subtraction of monomials and other polynomials.
Example: Subtract 5x from 3x.
Vertically: 3x 3x
-+ 5x - 5x
- 2x
Horizontally: 3x – 5x + 3x + (-5x) = -2x
Note: it is important that you determine whether your subtrahend is negative or positive. Written
horizontally as in – 7y -8y, the sign between the terms is a sign of operation. Thus it means that you
will deduct +8 from -7. Therefore, to subtract, you add -8 to -7.
Example: (a+ b) – (a – b) = (a + b) + (-a + b)
= a + (-a) + b + b
= 2b
Note
1. As in addition, the difference between unlike terms can only be indicated
2. For subtraction of polynomials, it is advisable to use vertical subtraction.
XII. MULTIPLICATION OF POLYNOMIALS
Powers of Monomials
A basic idea of base, powers, and exponents is a prerequisite to multiplication of monomials and
polynomials. What shortcut would you use to find the sum of 4 + 4 + 4 + 4 + 4? How would you
state this as a multiplication problem? Similarly, Instead of multiplying 2 x 2 x 2 x 2 x 2, we can
raise to its 5th
power and denote it by 25
= 32, where 2 is the base, 5 is the exponent, and 32 is the
power.
(The second column is done mentally,
think: the additive inverse of 5sx is –
5x. Adding 3x to – 5x gives – 2x)
LE 1
Xn
• xm
= xm + n

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A. Multiplying of Monomials
Consider the following illustrative types of multiplying monomial.
Example:
1. 4(x) = 4x
2. X • y • z = xyz
3. (3a)(3b)(4c) = (3.3.4) (a.b.c) = 36 abc
4. x •x2
= x1+2
= x3
5. (3x)(x2
) = 3 (x) (x2
) = 3x3
6. (5x2
)(3y)(2x) = (5 •2 • 3) (x2
• x • y) = 30x3
y
7. (2xy) (4x2
y3
) = (2 • 4) (x • x2
• y • y3
) = 8x3
y4
B. Multiplying Polynomials by a Monomial
Multiplication of a polynomial by a monomial makes use of the distributive property of
multiplication over addition. Remember that by the distributive property we have.
3 (6 + 5) = 3(6) + 3(5)
= 18 + 15
= 33
Now if we let 3 = a, 6 = b, 5 = c, then we get::
3(6 + 5) = 3(6) + 3(5)
a(b + c) = a(b) + a(c)
= ab + ac
C. Multiplying a Polynomial by Another Polynomial
The use of the distributive property can be extended to the multiplication of multinomial.
Study the following cases and observe clearly how the distributive property is used to the
advantage.
Key Concept
 To multiply two or more monomials, multiply the coefficients; the exponents
of the literal coefficients in the product will be the sum of these exponents of
the same base.

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Example 1: (x + 2) (x + 3)
a (b + c) = a(b) = a(c)
(x+ 2) (x + 3) = (x + 2) (x) + (x + 2) (3)
= x + 2x + 3x + 6
Example 2: (x + 2) (x + 3) solved vertically
x + 2
x + 3
x2
+ 2x x(x +2) partial product
3x + 6 3(x + 2) partial product
X + 5x + 6 Answer complete product
XIII. DIVISION ON POLYNOMIALS
Division monomials will be easy as long as you bear in mind that division is just the inverse process
of multiplication and that it is the process of looking for a missing fator.
Examples:
1. X5
= x • x • x • x • x = x2
x3
x • x • x
2. a2
b c3
= a
a b2
c3
b
LE-2 (am
)n
= amn
LE-3 (ab)m
= am
bm
(am
bm
)n
= amn
mmn

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Dividing a Polynomial by a Monomial
Dividing a polynomial by a monomial also employs the distributive property as well as definition of
division. Consider the examples below,
Example 1: Using the distributive property:
18x4
– 24x3
+ 6x2
= 18x4
- 24x3
+ 6x2
6x2
6x2
6x2
6x2
= 3x2
– 4x + 1
Example 2: using the definition as the process of multiplying the dividend by reciprocal of the
division:
(1/6x) (18x4
– 24x3
+ 6x2
) = 3x – 4x + 1
Dividing a polynomial by Another Polynomial
To make the process of dividing polynomials clearer, let us recall the algorithm of long division in
arithmetic. Let us divide 17,550 by 54
divisor
300 + 20 + 5
54 17550 dividend
54 x 300 16200
1350
54 x 20 1080
270
54 x 5 270
0
Actually when you divide 17,550 by 54, you are in fact subtracting 54 (300 + 20 + 5) from the
dividend. If the product of the divisor and the quotient is equal to the dividend, then the division is
exact and the remainder is zero. Note that you are subtracting a series of multiples of the divisor
until you exhaust the dividend. The same thing happens in the division of polynomials.

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Watch how it is done.
Example 1
Divide x3
– 7x2
+ 4x + 102 by x + 3
X2
– 10x + 34
x + 3 x3
– 7x2
+ 4x + 102
x (x + 3) x3
+ 3x2
- 10x2
+ 4x
-10x(x + 3) - 10x(x + 3)
34x + 102
34 (x + 3) 34(x + 3)
0
Example 2:
x2
+ 7x + 21 +55
x – 3 x3
+ 4x2
+ 0x – 8 x - 3
x3
– 3x2
7x + 0x
7x – 21x
21x – 8
21x – 63
55
XIV. SIMPLIFYING EXPRESSIONS
Simplification of an algebraic expression is the process of arriving at an equivalent expression
which is simpler than the given original expression. Armed with your knowledge of properties of
numbers and your computational skill in operations involving polynomials, simplification of
algebraic expressions should be an easy job for you.
Examples:
Collect and express results in the simplest form:
1. 6a + a 3b + 4b
(6a + a) + (3b + 4b) = 7a + 7b
2. (2a + b) + (a + b) + (3a – 3b)
2a + b
a + b
3a – 3b
6a - b

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3. -2(c + 4) – 5(c + 4)
= -2c – 8 – 5c – 20
= -7c – 28
4. When there is more than one grouping symbol begin by removing the innermost grouping
symbol and continue to do so until all grouping symbols have been removed.
5[ 3a – (a + )] = 5 [3a – a – 2]
= 5 (2a – 2)
= 10a – 10
5. 3 – [2a + {3a – (5a -4) + 6a} – 4a]
= 3 – (2a + {3a – 5a + 4 + 6a} – 4a
= 3 – {2a + 3a – 5a + 4 + 6a – 4a}
= 3 – 2a – 3a + 5a – 4 – 6a + 4a
= - 2a – 1

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XV. POST TEST
I. Write the letter of the best answer.
1. The property of real numbers which states that a + b = b + a
a. Symmetry
b. Identity property of addition
c. Commutative property of addition
d. Closure property
2. The number of variable which is taken as a factor one or more times by itself
a. Exponent c. Radica
b. Power d. Base
3. x + 2x – 2 is an example of
a. linear trinomial c. quartic
b. quadratic trinomial d. quadratic binomial
4. if you know the sum of two numbers and one of the numbers, what you are going to
do to find the other number.
a. Subtract c. Multiply
b. Add d. Divide
5. An algebraic expression which states a rule.
a. An equality c. A polynomial
b. An open phrase d. A formula
6. The leading monomial in 5x2
+ 3x4
– 7x + 2x5
+ 6x3
a. 5x2
c. 2x5
b. -7x d. 6x2
7. The exponent of the product of ax
ay
a. Xy c. yx
b. X + y d. x – y
8. The value of k that will make the sentence true; bk
• b = b5
a. 5 c. 3
b. 4 d. 6
9. The value of (2x2
)3
a. 2x6
c. 8x4
b. 6x6
d. 2x5
10. The numerical value of 2x3
z2
, if x = 1 andz = -3
a. -18 c. -54
b. 18 d. 54

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II. Perform the indicated operations.
1. 6xy + (-8xy) + 2xy
2. -7b + 8c + 10b – 20c
3. (x +y) + (2x – y)
4. (3x2
– 2x – 5) + (6x – 7) + (1 + x + x2
)
5. (3 – a2
) + (2a + 4a2
) + (a – 7 – 3a2
)
6. Subtract – 8c from – 12c
7. 16xy – (5xy)
8. What will you add to a2
+7 to get a2
-5a – 27
9. (2y3
– 5y – 7y2
) – (2y3
+ 6y2
– 8y)
10. Subtract x – y – z from x + y and from this result subtract 2x – 3y + 5z
III. Answer the following exercises:
A. Find the value when x = 3, y = -2, and z = 4.
1. X2
– y2
2. 2xy – ya 3. (4x2
– 2z) / y
B. 1. In ⁰C = 5/9 (⁰F – 32), find C if F is 104⁰
2. In A = ½ h(b + b), find A if h = 6, b = 8, and b = 10
IV. Simplify.
1. -3 (-2a4
)2
2. (-2x)(3x)3
3. A(2a – 3b) – 2b(7a – 3b)
4. 5m – {4a – 3(m + a)}
5. 5[3x – 7(x – 1)] – (x + 4)
XV. REFERENCE
MATHEMATICS II
BASIC ALGEBRA FOR SECONDARY SCHOOLS
Revised Edition
Numidas O Limjap
Carmen R. del Peña
Coordinator

Sem 2014 EDU 52
Answer Key
PRE TEST
Test 1
a. commutative property c. distributive property e. associative property
b. distributive property d. distributive property
Test 2
a. – c. - e. -
b. + d. - f. –
Test 3
a. -43 f. 5 k. 72
b. 8 g. -31 l. 0
c. -6 h. 28 m. 32
d. -18 i. 22 n. -64
e. -8 j. -3 0. 5
Test 4
a. numerical phrase d. open sentence g. numerical sentence
b. numerical phrase e. numerical sentence
c. numerical sentence f. arithmetical sentence
Test 5 Arithmetical and numerical
Test 6 Numerical phrase
Test 7 Numerical sentence
Test 8 Open sentence
POST TEST
Test I
1. c 6. d
2. d 7. a
3. b 8. a
4. d 9. c
5. d 10. A
Test II.
1. 6xy -8xy + 2xy + 0 6. -20c
2. 3b – 12 c 7. 21xy
3. 3x 8. -5a - 9
4. 4x2
+ 5x – 11 9. -13y2
+ 3y
5. 3a – 4 10. -2x + 5y – 3z
Test III.
1. 5
2. 2a -12
3. -14
Test IV.
1. 40 ⁰C
2. 54

Sem 2014 EDU 52

Module For Mathematics

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