4x^4-20x^2y^2+16y^4快~~~~~~~~~~~~~~~下面还有！！！！！！！！！！！！
答案:1 悬赏:50 手机版
解决时间 2021-11-17 19:13
- 提问者网友：趣果有间
- 2021-11-17 12:32
4x^4-20x^2y^2+16y^4快~~~~~~~~~~~~~~~下面还有！！！！！！！！！！！！
最佳答案
- 五星知识达人网友：西岸风
- 2021-11-17 13:43
解：
4x^4-20x²y²+16y^4
=4(x^4-5x²y²+4y^4)
=4(x²-y²)(x²-4y²)
=4(x+y)(x-y)(x+2y)(x-2y)
(3x²+2x+1)²-(2x²+3x+3)²
=[(3x²+2x+1)+(2x²+3x+3)][(3x²+2x+1)-(2x²+3x+3)]
=(3x²+2x+1+2x²+3x+3)(3x²+2x+1-2x²-3x-3)
=(5x²+5x+4)(x²-x-2)
=(5x²+5x+4)(x+1)(x-2)
(x²-3)²-4x²
=(x²-3)²-(2x)²
=[(x²-3)+2x][(x²-3)-2x]
=(x²+2x-3)(x²-2x-3)
=(x-1)(x+3)(x+1)(x-3)
4x^4-20x²y²+16y^4
=4(x^4-5x²y²+4y^4)
=4(x²-y²)(x²-4y²)
=4(x+y)(x-y)(x+2y)(x-2y)
(3x²+2x+1)²-(2x²+3x+3)²
=[(3x²+2x+1)+(2x²+3x+3)][(3x²+2x+1)-(2x²+3x+3)]
=(3x²+2x+1+2x²+3x+3)(3x²+2x+1-2x²-3x-3)
=(5x²+5x+4)(x²-x-2)
=(5x²+5x+4)(x+1)(x-2)
(x²-3)²-4x²
=(x²-3)²-(2x)²
=[(x²-3)+2x][(x²-3)-2x]
=(x²+2x-3)(x²-2x-3)
=(x-1)(x+3)(x+1)(x-3)
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