Question

Factorise:a4+2a3b-2ab3-b4..

Answer 1

$a^4+2a^3b-2ab^3-b^4\\\\=a^4-b^4+2a^3b-2ab^3\\\\=(a^2-b^2)(a^2+b^2)+2ab(a^2-b^2)\\\\=(a^2-b^2)(a^2+b^2+2ab)\\\\=(a-b)(a+b)(a+b)^2\\\\=(a-b)(a+b)(a+b)(a+b)$


$(x+y)^2=x^2+2xy+y^2\\\\x^2-y^2=(x-y)(x+y)$