因式分解

x^3-6x^2y+9xy^2-4y^3 x^4+2x^3y-3x^2y^2-4xy^3+4y^4

全部回答

2012-10-21

0 0

$$$$$$$$$$$$$$ x^3-6x^2y+9xy^2-4y^3 =(x^3-6x^2y+5xy^2)+(4xy^2-4y^3) =x(x-y)(x-5y)+4y^2(x-y) =(x-y)(x-y)(x-4y) x^4+2x^3y-3x^2y^2-4xy^3+4y^4 =(x^4+2x^3y-3x^2y^2)-(4xy^3-4y^4) =x^2(x-y)(x+3y)-4y^3(x-y) =(x-y)^2(x+2y)^2 。

提交

l***

2012-10-21

76 0

x³-6x²y+9xy²-4y³ =x³-6x²y+5xy²+4xy²-4y³ =x(x²-6xy+5y²）+（4xy²-4y³） =x(x-5y)(x-y)+4y²（x-y) =(x-y)(x²-5xy+4y²） =（x-y)(x-y)(x-4y) =(x-y)²（x-4y) x⁴+2x³y-3x²y²-4xy³+4y⁴ =(x⁴+2x³y-3x²y²)-（4xy³-4y⁴） =x²（x²+2xy-3y²）-4y³（x-y) =x²（x-y)(x+3y）-4y³（x-y) =(x-y)(x³+3x²y-4y³） =（x-y)(x³+3x²y+2xy²-2xy²-4y³） =（x-y)[x(x²+3xy+2y²）-2y²（x+2y)] =(x-y)[x(x+y)(x+2y)-2y²（x+2y)] =(x-y)(x+2y)(x²+xy-2y²） =（x-y)²（x+2y)²。
。

提交