Question

因式分解ax^3y+axy^3-2ax^2y^2

(x-1)(x-2)-2(2-x)^2; (a^2+ab+b^2)^2-9a^2b^2

Answer 1

ax³y+axy³-2ax²y²
=axy(x²+y²-2xy)
=axy(x-y)²

(x-1)(x-2)-2(2-x)²
=(x-2)[(x-1)-2(x-2)]
=(x-2)(x-1-2x+4)
=(x-2)(3-x)

(a²+ab+b²)²-9a²b²
=(a²+ab+b²-3ab)(a²+ab+b²+3ab)
=(a-b)²(a²+4ab+b²)

Answer 2

ax³y+axy³-2ax²y²
=axy(x²+y²-2xy)
=axy(x-y)²

Answer 3

2