题目

1.x的二次方（x+1）-y的二次方（y-1）+xy
2.p(p+1)(p-1)-q(q+1)(q-1)

提问时间：2021-03-12

答案

1.x的二次方（x+1）-y的二次方（y-1）+xy
=x²(x+1)-y²(y-1)+xy
=x³+x²-y³+y²+xy
=x³-y³+x²+xy+y²
=(x-y)(x²+xy+y²)+x²+xy+y²
=(x²+xy+y²)(x-y+1)
2.p(p+1)(p-1)-q(q+1)(q-1)
=p(p²-1)-q(q²-1)
=p³-p-q³+q
=p³-q³-p+q
=(p-q)(p²+pq+q²)-(p-q)
=(p-q)(p²+pq+q²-1)