Question

两道因式分解

问个因式分解的问题
题目如下（X的平方=X^2 X的三次方=X^3)

1. (ax+b)^2+(bx-cy)^2

2. xy(x^2-y^2)+yz(y^2-z^2)+zx(z^2-x^2)

大家速度回答啊
加分了
大家快回答啊

Answer 1

1. (ax+b)^2-(bx-cy)^2
=(ax+b+bx-cy)(ax+b-bx+cy)

2.xy(x^2-y^2)+yz(y^2-z^2)+zx(z^2-x^2)
=x^3y-xy^3+y^3z-yz^3+z^3x-zx^3
=x^3(y-z)+y^3(z-x)+z^3(x-y)
=x^3(y-z)+y^3(z-x)+z^3[(x-z)+(z-y)]
=(x^3-z^3)(y-z)+(y^3-z^3)(z-x)
=(x-z)(x^2+xz+z^2)(y-z)+(y-z)(y^2+yz+z^2)(z-x)
=(x-z)(y-z)(x^2+zx+z^2-y^2-yz-z^2)
=(x-z)(y-z)(x-y)(x+y+z)

Answer 2

xy(x²-y²)+yz(y²-z²)+zx(z²-x²)
=x³y-xy³+y³z-yz³+z³x-zx³
=x³(y-z)+y³(z-x)+z³(x-y)
=x³(y-x+x-z)+y³(z-x)+z³(x-y)
=x³(y-x)+x³(x-z)+y³(z-x)+z³(x-y)
=y³(z-x)-x³(z-x)+z³(x-y)-x³(x-y)
=(z-x)(y³-x³)+(x-y)(z³-x³)
=(z-x)(y-x)(y²+xy+x²)-(y-x)(z-x)(z²+xz+x²)
=(z-x)(y-x)[(y²+xy+x²)-(z²+xz+x²)]
=(z-x)(y-x)[(y²-z²)+(xy-xz)]
=(z-x)(y-x)[(y-z)(y+z)+x(y-z)]
=(z-x)(y-x){(y-z)[(y+z)+x]}
=(z-x)(y-x)(y-z)(x+y+z)

Answer 3

1、(ax+b+bx-cy)(ax+b-bx+cy)

2、(y-z)*(-z+x)*(x-y)*(x+z+y)

Answer 4

分太少了