（ay+bx）^3-(ax+by)^3+(a^3-b^3)(x^3-y^3)因式分解

Question

（ay+bx）^3-(ax+by)^3+(a^3-b^3)(x^3-y^3)
因式分解

Answer 1

（ay+bx）^3-(ax+by)^3+(a^3-b^3)(x^3-y^3)
=(ay+bx-ax-by)((ay+bx)^2+(ay+bx)(ax+by)+(ax+by)^2+(a-b)(a^2+ab+b^2)(x-y)(x^2+xy+y^2))
=(a-b)(x-y)((a^2+ab+b^2)(x^2+xy+y^2)-(ay+bx)^2-(ax+by)(ay+bx)-(ax+by)^20
=(a-b)(x-y)(a^2x^2+a^2xy+a^2y^2+x^2ab+abxy+aby^2+b^2x^2+b^2xy+b^2y^2-a^2y^2-2abxy-b^2x^2-a^2xy-abx^2-aby^2-b^2xy-a^2x^2-2abxy-b^2y^2)
=-3abxy(a-b)(x-y)
=3abxy(a-b)(y-x)