Question

定义一种新运算：a*b=ab+a^2-b^2,那么(x+y)*(x-y)=_____

Answer 1

(x+y)*(x-y)=(x+y)(x-y)+ (x+y)(x+y) - (x-y)(x-y) = x^2-y^2+4xy
其实就是将(x+y)当做a，（x-y）当做b带入到ab+a^2-b^2，然后展开整理就得到了

Answer 2

即a=x+y,b=x-y
所以(x+y)*(x-y)
=（x+y)(x-y)+(x+y)²-(x-y)²
=x²-y²+x²+2xy+y²-x²+2xy-y²
=x²+4xy-y²