(2x+y)^3-(x-2y)^3因式分解
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/01 23:20:20
(2x+y)^3-(x-2y)^3因式分解
![(2x+y)^3-(x-2y)^3因式分解](/uploads/image/z/17786011-67-1.jpg?t=%282x%2By%29%5E3-%28x-2y%29%5E3%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3)
原式=【(2x+y)-(x-2y)][(2x+y)^2+(2x+y)(x-2y)+(x-2y)^2]
=(x+3y)(4x^2+4xy+y^2+2x^2-3xy-2y^2+x^2-4xy+4y^2)
=(x+3y)(7x^2-3xy+3y^2)
=(x+3y)(4x^2+4xy+y^2+2x^2-3xy-2y^2+x^2-4xy+4y^2)
=(x+3y)(7x^2-3xy+3y^2)