一道初一数学题(用平方差公式解)
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一道初一数学题(用平方差公式解)
(x-y+z)²-(x+y-z)²
(x-y+z)²-(x+y-z)²
![一道初一数学题(用平方差公式解)](/uploads/image/z/5313077-53-7.jpg?t=%E4%B8%80%E9%81%93%E5%88%9D%E4%B8%80%E6%95%B0%E5%AD%A6%E9%A2%98%EF%BC%88%E7%94%A8%E5%B9%B3%E6%96%B9%E5%B7%AE%E5%85%AC%E5%BC%8F%E8%A7%A3%EF%BC%89)
(x-y+z)²-(x+y-z)²
=[(x-y+z)+(x+y-z)][(x-y+z)-(x+y-z)]
=(x-y+z+x+y-z)(x-y+z-x-y+z)
=2x × (-2y+2z)
=-4xy+4xz
=-4x(y-z)
=[(x-y+z)+(x+y-z)][(x-y+z)-(x+y-z)]
=(x-y+z+x+y-z)(x-y+z-x-y+z)
=2x × (-2y+2z)
=-4xy+4xz
=-4x(y-z)