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

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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
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

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
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)

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)

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)