利用公式计算(x+y-z)(x-y+z)-(x+y+z)(x-y-z)

Question

利用公式计算(x+y-z)(x-y+z)-(x+y+z)(x-y-z)

Answer 1

用平方差公式(a-b)(a+b)=a^2-b^2,则(x+y-z)(x-y+z)化为[x-(y-z)][x-(y-z)]=x^2-(y-z)^2,同理,(x+y+z)(x-y-z)=x^2+(y+z)^2,相减得(y+z)^2-(y-z)^2,再反着用次这公式,最后等于4yz.＜我用手机写的,可能会算错,但方法肯定对＞