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=x

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)