分组分解法 1）9m^2-6m+2n-n^2 2）4x^2+1/4-9y^2-2x 3) (ab+1)^2-(a+b)^2 4) (z^2-x^2-y^2)^2-4x^2y^2
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解决时间 2021-01-08 18:22
- 提问者网友：缘字诀
- 2021-01-07 22:42
分组分解法 1）9m^2-6m+2n-n^2 2）4x^2+1/4-9y^2-2x 3) (ab+1)^2-(a+b)^2 4) (z^2-x^2-y^2)^2-4x^2y^2
最佳答案
- 五星知识达人网友：末日狂欢
- 2021-01-07 23:54
1）9m²-6m+2n-n²
=9m²-6m+1-(n²-2n+1)
=(3m-1)²-(n-1)²
=(3m-1+n-1)(3m-1-n+1)
=(3m+n-2)(3m-n)
2）4x²+1/4-9y²-2x
=4x²-2x+1/4-9y²
=(2x-1/2)²-9y²
=(2x-1/2 +3y)(2x-1/2 -3y)
=(1/4)(4x+6y-1)(4x-6y-1)
3) (ab+1)²-(a+b)²
=(ab+1+a+b)(ab+1-a-b)
=(a+1)(b+1)(1-a)(1-b)
4) (z²-x²-y²)²-4x²y²
=(z²-x²-y²+2xy)(z²-x²-y²-2xy)
=[z²-(x-y)²]*[z²-(x+y)²]
=(z+x-y)(z-x+y)(z+x+y)(z-x-y)
=9m²-6m+1-(n²-2n+1)
=(3m-1)²-(n-1)²
=(3m-1+n-1)(3m-1-n+1)
=(3m+n-2)(3m-n)
2）4x²+1/4-9y²-2x
=4x²-2x+1/4-9y²
=(2x-1/2)²-9y²
=(2x-1/2 +3y)(2x-1/2 -3y)
=(1/4)(4x+6y-1)(4x-6y-1)
3) (ab+1)²-(a+b)²
=(ab+1+a+b)(ab+1-a-b)
=(a+1)(b+1)(1-a)(1-b)
4) (z²-x²-y²)²-4x²y²
=(z²-x²-y²+2xy)(z²-x²-y²-2xy)
=[z²-(x-y)²]*[z²-(x+y)²]
=(z+x-y)(z-x+y)(z+x+y)(z-x-y)
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