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因式分解x^3+3x^2y+3xy^2+2y^3
题目详情
因式分解x^3+3x^2y+3xy^2+2y^3
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答案和解析
x^3+3x^2y+3xy^2+2y^3
=x^3+y^3+3x^2y+3xy^2+y^3
=(x^3+y^3)+(3x^2y+3xy^2)+y^3
=(x+y)(x^2-xy+y^2)+3xy(x+y)+y^3
=(x+y)(x^2-xy+y^2+3xy)+y^3
=(x+y)(x^2+2xy+y^2)+y^3
=(x+y)(x+y)^2+y^3
=(x+y)^3+y^3
=[(x+y)+y][(x+y)^2-y(x+y)+y^2]
=(x+2y)(x^2+2xy+y^2-xy-y^2+y^2)
=(x+2y)(x^2+xy+y^2)
=x^3+y^3+3x^2y+3xy^2+y^3
=(x^3+y^3)+(3x^2y+3xy^2)+y^3
=(x+y)(x^2-xy+y^2)+3xy(x+y)+y^3
=(x+y)(x^2-xy+y^2+3xy)+y^3
=(x+y)(x^2+2xy+y^2)+y^3
=(x+y)(x+y)^2+y^3
=(x+y)^3+y^3
=[(x+y)+y][(x+y)^2-y(x+y)+y^2]
=(x+2y)(x^2+2xy+y^2-xy-y^2+y^2)
=(x+2y)(x^2+xy+y^2)
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