分解因式:x^2(x+1)-y(xy+x)

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分解因式:x^2(x+1)-y(xy+x)
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分解因式:x^2(x+1)-y(xy+x)
分解因式:x^2(x+1)-y(xy+x)

分解因式:x^2(x+1)-y(xy+x)
x^2(x+1)-y(xy+x)
=x^3+x^2-xy^2-xy
=x(x^2-y^2)+x(x-y)
=x(x-y)(x+y)+x(x-y)
=x(x-y)(x+y+1)

解: x^2(x+1)-y(xy+x)
=x^2(x+1)-xy(y+1)
=x[x(x+1)-y(y+1)]
=x(x^2+x-y^2-y)
=x[(x^2-y^2)+(x-y)]
=x[(x+y)(x-y)+(x-y)]
=x(x-y)(x+y+1)