Question

What is the factored form of 8x^24-27y^6

Answer 1

The factored form of that expression is,
(2x^8-3y^2)(4x^16+6x^8y^2+9y^4).

Answer 2

Answer:  The required factored form of the given expression is $(2x^8-3y^2)(4x^{16}+6x^8y^2+9y^4).$

Step-by-step explanation:  We are given to find the factored form of the following expression :

$E=8x^{24}-27y^6.$

We will be using the following factorization formula :

$a^3-b^3=(a-b)(a^2+ab+b^2).$

So, the factorization of the given expression is as follows :

$E\\\\=8x^{24}-27y^6\\\\=(2x^8)^3-(3y^2)^3\\\\=(2x^8-3y^2)((2x^8)^2+2x^8\times3y^2+(3y^2)^2)\\\\=(2x^8-3y^2)(4x^{16}+6x^8y^2+9y^4).$

Thus, the required factored form of the given expression is $(2x^8-3y^2)(4x^{16}+6x^8y^2+9y^4).$