Factorasitation

Question

2x^6-16y^6-8x^2y^4+4x^4y^2

Answer 1

First note that a³-b³=(a-b)(a²+ab+b²). Now let a=x² and b=2y², then a³-b³=x⁶-8y⁶=(x²-2y²)(x⁴+2x²y²+4y⁴).

2x⁶-16y⁶-8x²y⁴+4x⁴y²=2(x⁶-8y⁶-4x²y⁴+2x⁴y²)=

2((x²-2y²)(x⁴+2x²y²+4y⁴)+2x²y²(x²-2y²))=2(x²-2y²)(x⁴+4x²y²+4y⁴)=2(x²-2y²)(x²+2y²)².