提取公因数——平方差公式法
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/07/29 18:06:38
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)
![提取公因数——平方差公式法](/uploads/image/z/17934943-31-3.jpg?t=%E6%8F%90%E5%8F%96%E5%85%AC%E5%9B%A0%E6%95%B0%E2%80%94%E2%80%94%E5%B9%B3%E6%96%B9%E5%B7%AE%E5%85%AC%E5%BC%8F%E6%B3%95)
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]