x^3(a+1)-xy(x-y)(a-b)+y3^(b+1) 因式分解
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x³(a+1)-xy(x-y)(a-b)+y³(b+1)
=x³(a-b+b+1)-xy(x-y)(a-b)+y³(b+1)
=x³(a-b)+x³(b+1)-xy(x-y)(a-b)+y³(b+1)
=(x³+y³)(b+1)+[x³-xy(x-y)](a-b)
=(x+y)(x²-xy+y²)(b+1)+x(x²-xy+y²)(a-b)
=(x²-xy+y²)[(x+y)(b+1)+x(a-b)]
=(x²-xy+y²)(ax+x+by+y)
=x³(a-b+b+1)-xy(x-y)(a-b)+y³(b+1)
=x³(a-b)+x³(b+1)-xy(x-y)(a-b)+y³(b+1)
=(x³+y³)(b+1)+[x³-xy(x-y)](a-b)
=(x+y)(x²-xy+y²)(b+1)+x(x²-xy+y²)(a-b)
=(x²-xy+y²)[(x+y)(b+1)+x(a-b)]
=(x²-xy+y²)(ax+x+by+y)
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x^3(a+1)-xy(x-y)(a-b)+y3^(b+1)
=x^3(a+1)-(x^2y-xy^2)(a-b)+y^3(b+1)
=x^3(a+1)-(x^2y-xy^2)a+(x^2y-xy^2)b+y^3(b+1)
=a(x^3-x^2y+xy^2)+b(x^2y-xy^2+y^3)+x^3+y^3
=ax(x^2-xy+y^2)+by(x^2-xy+y^2)+(x+y)(x^2-xy+y^2)
=(x^2-xy+y^2)(ax+by+x+y)
=x^3(a+1)-(x^2y-xy^2)(a-b)+y^3(b+1)
=x^3(a+1)-(x^2y-xy^2)a+(x^2y-xy^2)b+y^3(b+1)
=a(x^3-x^2y+xy^2)+b(x^2y-xy^2+y^3)+x^3+y^3
=ax(x^2-xy+y^2)+by(x^2-xy+y^2)+(x+y)(x^2-xy+y^2)
=(x^2-xy+y^2)(ax+by+x+y)
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