1. Multiplying
Polynomials
Module 9 - Topic 2
Part 1

2. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
( 2
3x 2x − 7x + 5 )
by the monomial
outside the
parenthesis.
The number of terms
inside the parenthesis
will be the same as
after multiplying.

3. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
will be the same as
after multiplying.

4. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
will be the same as
after multiplying.

5. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
2
(
3x 2x − 7x + 5 2
)
will be the same as
after multiplying.

6. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
2
(
3x 2x − 7x + 5 2
)
will be the same as 4
6x − 21x + 15x 3 2
after multiplying.

7. Multiply a Polynomial by a
Monomial
Review this Cool Math site to learn about
multiplying a polynomial by a monomial.
Do the Try It and Your Turn problems in
your notebook and check your answers on
the next slides.

8. Try It - Page 1
Multiply: 4
(
6x 2x + 32
)

9. Try It - Page 1
Multiply: 4
(
6x 2x + 32
)
Distribute the monomial.

10. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3

11. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3
Multiply each term.

12. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3
Multiply each term.
6 4
12x + 18x

13. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3
Multiply each term.
6 4
12x + 18x
Verify your answer has same number of terms
as inside original ( ). Both have 2 terms.

14. Your Turn - Page 2
multiply:

15. Your Turn - Page 2
multiply:
3
( 5 2
10x 2x + 1 − 3x + x )

16. Your Turn - Page 2
multiply:
3
( 5 2
10x 2x + 1 − 3x + x )
Distribute the monomial.

17. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x5 2
)
Distribute the monomial.
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3

18. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
Multiply each term.

19. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x 5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
Multiply each term. 8 3 5 4
20x + 10x − 30x + 10x

20. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x 5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
8 3 5 4
Put in descending 20x + 10x − 30x + 10x
order and verify
number of terms.
(Both have 4 terms.)

21. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x 5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
8 3 5 4
Put in descending 20x + 10x − 30x + 10x
order and verify
number of terms. 8 5 4 3
(Both have 4 terms.)
20x − 30x + 10x + 10x

22. Try It - Page 2
Multiply:
2 5
( 2 2 4
4x w w − x + 6xw − 1 + 3x w 8
)

23. Try It - Page 2
Multiply:
2 5
( 2 2 4
4x w w − x + 6xw − 1 + 3x w 8
)
Distribute the monomial.

24. Try It - Page 2
Multiply:
2 5
(
4x w w − x + 6xw − 1 + 3x w 2 2 4 8
)
Distribute the monomial.
5
( 2
) 2 5
( 2
)
4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w
2 5 2 2 5 2 5
( 4 8
)

25. Try It - Page 2
Multiply:
2 5
(
4x w w − x + 6xw − 1 + 3x w 2 2 4 8
)
5
( 2
) 2 5
( 2
)
4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w
2 5 2 2 5 2 5
( 4 8
)
Multiply each term.

26. Try It - Page 2
Multiply:
2 5
(
4x w w − x + 6xw − 1 + 3x w 2 2 4 8
)
5
( 2
)
4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w
2 5 2 2 5
( 2
) 2 5 2 5
( 4 8
)
Multiply each term.
2 6 4 5 3 7 2 5 6 13
4x w − 4x w + 24x w − 4x w + 12x w
Verify answer has 5 terms like original parenthesis.

27. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )

28. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
Distribute the monomial.

29. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
Distribute the monomial.
( )
3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 )
2

30. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
( )
3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 )
2
Multiply each term.

31. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
( )
3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 )
2
Multiply each term.
3 2
6x − 15x + 21x

32. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b2 3 5
)

33. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
Distribute the monomial.

34. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
Distribute the monomial.
( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b )
2 2 3 2 2 2 3 2 2 5

35. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b )
2 2 3 2 2 2 3 2 2 5
Multiply each term.

36. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b )
2 2 3 2 2 2 3 2 2 5
Multiply each term.
5 2 4 5 2 7
−2a b − 6a b + 8a b

37. Great job working
all those problems!
Proceed to Part 2.