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因式分解练习(最好简单的写一下过程)

来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/30 20:13:50
因式分解练习(最好简单的写一下过程)
2(x-1)^2-x+1
-a^4+2a^2b^2-b^4
(x+2y)^2-4(x-3y)^2
9(2x-y)^2-6(2x-y)+1
(m^2-6m)^2+18(m^2-6m+81)
-12a(a-b)^3+6a^2(b-a)^3
因式分解练习(最好简单的写一下过程)
2(x-1)²-x+1
=2(x-1)²-(x-1)
=(x-1)[2(x-1)-1]
=(x-1)(2x-2-1)
=(x-1)(2x-3)
-a⁴+2a²b²-b⁴
=-(a⁴-2a²b²+b⁴)
=-(a²-b²)²
=-[(a+b)(a-b)]²
=-(a+b)²(a-b)²
(x+2y)²-4(x-3y)²
=[(x+2y)+2(x-3y)][(x+2y)-2(x-3y)]
=[x+2y+2x-6y][x+2y-2x+6y]
=(3x-4y)(8y-x)
9(2x-y)²-6(2x-y)+1
=[3(2x-y)-1]²
=(6x-3y-1)²
题目有问题,仔细看一下:
(m²-6m)²+18(m²-6m)+81
=[(m²-6m)+9]²
=[(m-3)²]²
=(m-3)⁴
-12a(a-b)³+6a²(b-a)³
=12a(b-a)³+6a²(b-a)³
=(b-a)³(12a+6a²)
=6a(b-a)³(2+a)