计算(x-y)^5,
1个回答
2013-07-05
展开全部
(x-y)(x-y)(x-y)(x-y)(x-y)
=(x²+2xy+y²)(x-y)(x-y)(x-y)
=(x³+3x²y+3xy²+y³)(x-y)(x-y)
=(x^4+4x³y+6x²y²+4xy³+y^4)(x-y)
=x^5+5x^4y+10x³y²+10x²y³+xy^4+y^5
=(x²+2xy+y²)(x-y)(x-y)(x-y)
=(x³+3x²y+3xy²+y³)(x-y)(x-y)
=(x^4+4x³y+6x²y²+4xy³+y^4)(x-y)
=x^5+5x^4y+10x³y²+10x²y³+xy^4+y^5
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