x^3+3x^2y+3y^2x-7y^3如何因式分解

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x^3+3x^2y+3y^2x-7y^3如何因式分解

x^3+3x^2y+3y^2x-7y^3如何因式分解
x^3+3x^2y+3y^2x-7y^3如何因式分解

x^3+3x^2y+3y^2x-7y^3如何因式分解
x^3+3x^2y+3y^2x-7y^3
=x^3+3x^2y+3y^2x+y^3-8y^3
=(x+y)^3-(2y)^3
=(x+y-2y)[(x+y)^2+2y(x+y)+(2y)^2]
=(x-y)(x^2+2xy+y^2+2xy+2y^2+4y^2)
=(x-y)((x^2+4xy+7y^2)

用到的2条公式:(a+b)^3=a^3+3a^2b+3ab^2+b^3
a^3-b^3=(a-b)(a^2+ab+b^2)

化简3(x-y)-7(x--y)+2(y-x) x(x-y)2-(y-x)3 [2/3x-2/x+y(x+y/3x-x-y)]/x-y/x 化简：{2/3x-2/(x+y)[(x+y)/3x-x-y]}/(x+y)/x 计算2/3x-2/x+y(x+y/3x-x-y)/x-y/x 化简3x-2/(x+y)[(x+y)/3x-x-y]÷(x-y)/x [(3x+y)(x-y)-(2x+3y)(x-y)]*(x-y) 计算：x+2y/x-y+2x/y-x-3y/x-y 化简:(x-3y)(x+y)-(x-2y)(x+2y)-(x-y)平方 (-3x+7y)(-7y-3x)-(x-3y)(2x+3y) 18(x+y)^8(x-y)^7÷[3(x+y)^3(x-y)^3]^2 3(x-y)^2-7(x-y)+8(y-x)^2+6(y-x)合并同类项. 2X(2X-3Y)-3Y(X+Y) (-2x y)^2-(3y-x)(-x-3y) 若(x-y)/(x+y)=3 则(x+2y)/(6x-7y)等于 计算：(x-y)^7÷(y-x)^6+(-x-y)^3÷(x+y)^2 2(y-x)的平方-7(x-y)+6(x-y)-3(y-x)的平方 计算(x-y)^7÷(y-x)^6+9-x-y)^3÷(x+y)^2