Answer: The required factored form of the given expression is [tex](2x^8-3y^2)(4x^{16}+6x^8y^2+9y^4).[/tex]
Step-by-step explanation: We are given to find the factored form of the following expression :
[tex]E=8x^{24}-27y^6.[/tex]
We will be using the following factorization formula :
[tex]a^3-b^3=(a-b)(a^2+ab+b^2).[/tex]
So, the factorization of the given expression is as follows :
[tex]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).[/tex]
Thus, the required factored form of the given expression is [tex](2x^8-3y^2)(4x^{16}+6x^8y^2+9y^4).[/tex]
