Question

How do you factor `36a ^ { 2} - 36a b - 27b ^ { 2}`?

Answer 1

9(2a - 3b)(2a + b)

Explanation:

Given, `36a^2-36ab-27b^2 = 9(4a^2-4ab-3b^2)`

`rArr 9(4a^2-6ab+2ab-3b^2)`

`rArr 9[2a(2a-3b)+b(2a-3b)]`

`rArr 9(2a-3b)(2a+b)`

Answer 2

`9(2a + b)(2a - 3b)`

Explanation:

`36a^2 - 36ab - 27b^2 = 9(4a^2 - 4ab - 3b^2)`
->`9` is a highest common factor for `36 and 27`

we try to find the product of factor for (4 * 3 = 12), then we get
`12 = 6 * 2, -6 + 2 = -4`
thereofore we replace `-4ab to -6ab + 2ab`

`9(4a^2 - 4ab - 3b^2) = 9(4a^2 -6ab + 2ab -3b^2)`
We separate into 2 portions and factor it.
1. `4a^2 - 6ab = 2a(2a - 3b)`
2. `2ab - 3b^2 = b(2a - 3b)`
it is correct when both of them have a same of `(2a - 3b)`,
therefore,
`(4a^2 -6ab + 2ab -3b^2) =2a(2a - 3b) +b(2a - 3b)= (2a + b)(2a - 3b)`

therefore,
`9(4a^2 -6ab + 2ab -3b^2) = 9(2a + b)(2a - 3b)`