分解因式:(p+q)3-3(p+q)2(p-q)+3(p+q)(p-q)2-(p-q)3.

问题描述:

分解因式:(p+q)3-3(p+q)2(p-q)+3(p+q)(p-q)2-(p-q)3

原式=[(p+q)3-(p-q)3]-[3(p+q)2(p-q)-3(p+q)(p-q)2]
=[(p+q)-(p-q)][(p+q)2+(p+q)(p-q)+(p-q)2]-3(p+q)(p-q)[(p+q)-(p-q)]
=2q[(p+q)2+(p+q)(p-q)+(p-q)2]-2q•3(p+q)(p-q)
=2q[(p+q)2-2(p+q)(p-q)+(p-q)2]
=2q[(p+q)-(p-q)]2
=2q•(2q)2
=8q3