提取公因数——平方差公式法
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提取公因数——平方差公式法
(1)(x+y)^3(x-y)-(x+y)(x-y)^3
(2)25(x-2y)^3+4(2y-x)
(1)(x+y)^3(x-y)-(x+y)(x-y)^3
(2)25(x-2y)^3+4(2y-x)
题1
(x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)[(x+y)^2-(x-y)^2]
=(x^2-y^2)(x^2+2xy+y^2-x^2+2xy-y^2)
=4xy(x^2-y^2)
=4xy(x+y)(x-y)
题2
25(x-2y)^3+4(2y-x)
=25(x-2y)^3-4(x-2y)
=(x-2y)[25(x-2y)^2-4]
=(x-2y)[5(x-2y)+2][5(x-2y)-2]
(x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)[(x+y)^2-(x-y)^2]
=(x^2-y^2)(x^2+2xy+y^2-x^2+2xy-y^2)
=4xy(x^2-y^2)
=4xy(x+y)(x-y)
题2
25(x-2y)^3+4(2y-x)
=25(x-2y)^3-4(x-2y)
=(x-2y)[25(x-2y)^2-4]
=(x-2y)[5(x-2y)+2][5(x-2y)-2]