3. Problem 1
9x2 - 4
3x(3x) 2(2)
Both of these can be squared so I will show you what
they are squared by under them. To make our problem
we will try to fit the formula a2 + b2 = (a + b)(a-b). Since
the first one is a2 (9x2), a is 3x, using this way of
thinking, I would say that b is 2. Our answer is on the
next page.
5. Example Problems
a2 – 81
36m2 – 25
4x2 – y2
a2 + 64
Remember that both must be PERFECT squares.
6. Example Problems
a2 – 81 (a + 9)(a – 9)
36m2 – 25 (6m + 5)(6m – 9)
4x2 – y2 (2x + y)(2x – y)
a2 + 64
This cannot be factored since this method doesn’t
work with addition problems, only subtraction.
7. Mini Lesson
If you feel you are just doing the problems
blindly, check them with F.O.I.L. and you will find
that two of the numbers cancel out together.
9. Problem 2
2a2 – 200
To make this problem work so that we have squares
we will have to divide it by 2.
a2 – 100
Now we can solve that to get (a + 10)(a – 10). We add
the 2 back by placing it next to the problem for
multiplication, making our final answer look like the
slide on the next page.
12. Problem 3
-4c2 + 36
To make this work we will remember what we did in
the last problem and divide the problem by -4, making
it c2 - 9. Solving this the normal way we will get
(c + 3)(c-3) which will change to be -4(c + 3)(c-3).
16. Problem 4
25x2+ 10x + 1
We will answer this using the formula on slide 13.
a2 + 2ab + b2 = (a + b)(a + b) or (a + b)2
25x2+ 10x + 1
We will first get the square root the 25x2 (5x) and place
it in the ‘a’ place of the formula. Then we will get the
square root of 1 (1) and place it in the ‘b’ place of the
formula. The answer will be on the next slide.
19. Problem 5
144y2 - 120y + 25
We need to find a way to accommodate the negative
sign in the middle so just blindly using our formula to
get (12y + 5)(12y + 5) won’t work. We can however,
make it (12y - 5)(12y – 5), which will achieve our goals
perfectly.
