因式分解,十字相乘2乘（x+y）的2次方减去5（x+y）(y-z)加2乘（y-z）的2次方..怎么算
问题描述：
因式分解,十字相乘
2乘（x+y）的2次方减去5（x+y）(y-z)加2乘（y-z）的2次方..怎么算
答
2(x+y)^2 -5(x+y)(y-z)+2(y-z)^2
=[(x+y)-2(y-z)][(2(x+y)-(y-z)]
=(x+y-2y+2z)(2x+2y-y+z)
=(x-y+2z)(2x+y+z)
答
2*（x+y）^2-5（x+y）(y-z)+2*（y-z）^2
=[2*（x+y）-（y-z）][（x+y）-2（y-z）]
=(2x+y+z)(x-y+2z)
答
令a=x+y,b=y-z
则原式=2a²-5ab+2b²
=(2a-b)(a-2b)
=(2x+2y-y+z)(x+y-2y+2z)
=(2x+y+z)(x-y+2z)