若(x的平方-y的平方)(x+y)=(x-y)(x的平方+axy+y的平方) 则a的值为（）
问题描述：
若(x的平方-y的平方)(x+y)=(x-y)(x的平方+axy+y的平方) 则a的值为（）
答
左边=(x+y)²(x-y)
=(x-y)(x²+2xy+y²)
所以a=2
答
(x^2-y^2)(x+y)=(x-y)(x^2+axy+y^2)
(x+y)(x-y)(x+y)=(x-y)(x^2+axy+y^2)
(x+y)^2=(x^2+axy+y^2)
(x^2+2xy+y^2)=(x^2+axy+y^2)
a=2
答
都分解开，就出来了，得A=2
答
(x²-y²)(x+y)=(x-y)(x²+axy+y²)
(x-y)(x+y)²-(x-y)(x²+axy+y²)=0
(x-y)[(x+y)²-(x²+axy+y²)]=0
(x-y)(x²+2xy+y²-x²-axy-y²)=0
(2-a)xy(x-y)=0
对于任意实数x，y，等式恒成立，只有2-a=0
a=2
答
(x^2-y^2)(x+y)
=(x-y)(x+y)(x+y)
=(x-y)(x+y)^2
=(x-y)(x^2+2xy+y^2)
=(x-y)(x^2+axy+y^2)
因此a=2
如果认为讲解不够清楚,