因式分解（x+Y+Z)²-(X-y-z)²和﹙a²+4﹚²－16a

题目

因式分解（x+Y+Z)²-(X-y-z)²和﹙a²+4﹚²－16a

答案

（x+Y+Z)²-(X-y-z)²
=(x+y+z+x-y-z)(x+y+z-x+y+z)
=2x*(2y+2z)
=4x(y+z)
﹙a²+4﹚²－16a²
=(a²+4-4a)(a²+4+4a)
=(a-2)²(a+2)²