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

Answer:

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

Step-by-step 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 $(2x+4y)(4x^2-8xy+16y^2)$.