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

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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因式分解ax^3y+axy^3-2ax^2y^2(x-1)(x-2)

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
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

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
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)

2

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