Question

因式分解，要过程谢谢

因式分解一。(m+n)(5a+4b-3)+(n+2m)(3-5a-4b) 二。3a²y-3ay+6y 三-4x³y+8x²y²-4xy³ 四。8x³-(x-y)³-(x+y)³

Answer 1

解: 一。(m+n)(5a+4b-3)+(n+2m)(3-5a-4b) 提取(3-5a-4b) 里的负号
=(m+n)(5a+4b-3)-(2m+n)(5a+4b-3) 提取公因式5a+4b-3
=(5a+4b-3)(m+n-2m-n) 合并同类项
=-m(5a+4b-3)

二。3a²y-3ay+6y 提取公因式3y
=3y(a²-a+6)
若式子是 3a²y-3ay-6y 感觉楼主抄错题了........
则 =3y(a²-a-6) 十字相乘法
=3y(a-3)(a+2)

三 -4x³y+8x²y²-4xy³ 提取公因式-4xy
=-4xy(x²-2xy+y²) 完全平方公式
=-4xy(x-y)²

四。8x³-(x-y)³-(x+y)³
=(2x)³-[(x-y)³+(x+y)³] 把x-y)³和(x+y)³ 看成整体用立法和公式
=(2x)³-{[(x-y)+(x+y)][(x-y)²-(x-y)(x+y)+(x+y)²] 套用立方和公式
=(2x)³-2x(x²-2xy+y²-x²+y²+x²+2xy+y²) 打开括号并化简
=(2x)³-2x(x²+3y²) 合并同类项
=2x(4x²-x²-3y²) 提取公因式2x
=2x(3x²-3y²) 再提取公式3
=6x(x+y)(x-y)
祝你学习进步,如有不明可以追问.同意我的答案请采纳,O(∩_∩)O谢谢

Answer 2

(m+n)(5a+4b-3)+(n+2m)(3-5a-4b)
=(m+n)(5a+4b-3)+(n+2m)[-(5a+4b-3)]
=(m+n)(5a+4b-3)+(-n-2m)(5a+4b-3)
=(5a+4b-3)[(m+n)+(-n-2m)]
=-m(5a+4b-3)

3a²y-3ay+6y
=3y(a²-a+2)

-4x³y+8x²y²-4xy³
=-4xy(x²-2xy+y²)
=-4xy(x-y)²

8x³-(x-y)³-(x+y)³
=8x³-(x-y)(x-y)²-(x+y)(x+y)²
=8x³-(x-y)(x²-2xy+y²)-(x²+2xy+y²)(x+y)
=8x³-(x³-3x²y+3xy²-y³)-(x³+3x²y+3xy²+y³)
=8x³-2x³-6xy²
=6x(x²-y²)
=6x(x+y)(x-y)

中学生数理化为你解答
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Answer 3

一。(m+n)(5a+4b-3)+(n+2m)(3-5a-4b)
=(m+n)(5a+4b-3)-(n+2m)(5a+4b-3)
=(5a+4b-3)(m+n-n-2m)
=-m(5a+4b-3)
二。3a²y-3ay+6y
=3y(a²-a+2)
三-4x³y+8x²y²-4xy³
=-4xy(x²-2xy+y²)
=-4xy(x-y)²
四。8x³-(x-y)³-(x+y)³
=8x³-[(x-y)³+(x+y)³]
=8x³-(x-y+x+y)[(x-y)²-(x-y)(x+y)+(x+y)²]
=8x³-2x(x²-2xy+y²-x²+y²+x²+2xy+y²)
=8x³-2x(x²+3y²)
=2x(4x²-x²-3y²)
=6x(x²-y²)
=6x(x+y)(x-y)