Question

Which of the following is the correct factorization of the polynomial below 8x^3+64y^3

Answer 1

8x^3+64y^3

factor out 8

8(x^3+y^3)

this is known as the sum of cubes

8(x + y) (x^2 - x y + y^2)

Answer 2

`(2x+4y)(4x^2-8xy+16y^2)`

Explanation:

We are asked to factor
`8x^3+64y^3`.

We can rewrite 8 as
`2^3` and 64 as
`4^3`.

`(2x)^3+(4y)^3`

Using sum of cubes
`a^3+b^3=(a+b)(a^2-ab+b^2)`, we will get:

`(2x)^3+(4y)^3=(2x+4y)((2x)^2-(2x*4y)+(4y)^2)`

`(2x)^3+(4y)^3=(2x+4y)(4x^2-8xy+16y^2)`

Therefore, the factored form of our given expression would be
`(2x+4y)(4x^2-8xy+16y^2)`.