Question

Which expression is the completely factored form of x6−64y3 ? (x2−4y)(x4−16y2) (x2−4y)3 (x2−4y)(x4+4x2y+16y2) (x2+4y)(x4−4x2y+16y2)

Answer 1

(x^2 - 4y)(x^4 + 4x^2 y + 16y^2)

Answer 2

The expression which is obtained on factorising it completely is:

`x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)`

Explanation:

We are asked to factorize the expression which is given by:

`x^6-64y^3`

This expression could also be written as:

`x^6-64y^3=(x^2)^3-(4y)^3`

Now, we know that:

`a^3-b^3=(a-b)(a^2+b^2+ab)`

Here we have:

`a=x^2\\\\and\\\\b=4y`

Hence,

`x^6-64y^3=(x^2-4y)((x^2)^2+(4y)^2+x^2* 4y)`

i.e.

`x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)`