Question

Factor these expressions into an equivalent form.

c^2 - 64

12y^2 - 75

ab^2 - b

Answer 1

(c+8)(c-8)

3(2y+5)(2y-5)

There are no like terms so it's still ab^2-b

Answer 2

a)

`c^2-64=(c-8)(c+8)`

b)

`12y^2-75=3(2y-5)(2y+5)`

c)

`ab^2-b=b(ab-1)`

Explanation:

a)

`c^2-64`

This expression could also be given by:

`c^2-8^2`

Now, we know that:

`a^2-b^2=(a-b)(a+b)`

Hence, we have:

`c^2-64=(c-8)(c+8)`

b)

`12y^2-75`

`12y^2-75=3(4y^2-25)`

which is further given by:

`12y^2-75=3((2y)^2-5^2)\\\\12y^2-75=3(2y-5)(2y+5)`

c)

`ab^2-b`

we take out common b from both the terms to get:

`ab^2-b=b(ab-1)`