Question

因式分解x^2(x^2-y^2)+z^(y^2-x^2)

步骤。
第三步怎么转变的

Answer 1

x^2(x^2-y^2)+z^2(y^2-x^2)
=x^2(x^2-y^2)-z^2(x^2-y^2)
=(x^2-z^2)(x^2-y^2) 这是提取公因式x^2-y^2
=(x+z)(x-z)(x+y)(x-y) 这是平方差

Answer 2

x^2(x^2-y^2)+z^2(y^2-x^2)
=x^2(x^2-y^2)-z^2(x^2-y^2)
=(x^2-z^2)*(x^2-y^2)
=(x+z)*(x-z)*(x+y)*(x-y)

Answer 3

x^2(x^2-y^2)+z^(y^2-x^2)
=x^2(x^2-y^2)-z^(x^2-y^2)
=(x^2-y^2)(x^2-z^2)
=(x+y)(x-y)(x+z)(x-z)