因式分解 (1)4a^4-64(2)x^4-18x^2y^2+81y^4(3)(x^2-y
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解决时间 2021-03-11 14:32
- 提问者网友：火车头
- 2021-03-10 16:51
因式分解 (1)4a^4-64(2)x^4-18x^2y^2+81y^4(3)(x^2-y
最佳答案
- 五星知识达人网友：白昼之月
- 2021-03-10 17:16
(1)
4a^4-64
=4(a^4-16)
=4(a^4-2^4)
=4(a^2+2^2)(a^2-2^2)
=4(a^2+2^2)(a+2)(a-2)
=4(a+2)(a-2)(a^2+2^2)
(2)
x^4-18x^2y^2+81y^4
=(x^2-9y^2)^2
=[(x+3y)(x-3y)]^2
=(x+3y)^2(x-3y)^2
(3)
(x^2-y)^2- (1-y)^2
=(x^2-y+1-y)(x^2-y-1+y)
=(x^2-2y+1)(x^2-1)
=(x^2-2y+1)(x+1)(x-1)
=(x+1)(x-1)(x^2-2y+1)
4a^4-64
=4(a^4-16)
=4(a^4-2^4)
=4(a^2+2^2)(a^2-2^2)
=4(a^2+2^2)(a+2)(a-2)
=4(a+2)(a-2)(a^2+2^2)
(2)
x^4-18x^2y^2+81y^4
=(x^2-9y^2)^2
=[(x+3y)(x-3y)]^2
=(x+3y)^2(x-3y)^2
(3)
(x^2-y)^2- (1-y)^2
=(x^2-y+1-y)(x^2-y-1+y)
=(x^2-2y+1)(x^2-1)
=(x^2-2y+1)(x+1)(x-1)
=(x+1)(x-1)(x^2-2y+1)
全部回答
- 1楼网友：空山清雨
- 2021-03-10 18:23
4a^4-64
=4(a^4-16)
=4(a²-4)(a²+4)
=4(a-2)(a+2)(a²+4)
x^4-18x²y²+81y^4
=(x²-9y²)²
=(x-3y)²(x+3y)²
(x²-y)²-(1-y)²
=(x²-y-1+y)(x²-y+1-y)
=(x²-1)(x²-2y+1)
=(x-1)(x+1)(x²-2y+1)
=4(a^4-16)
=4(a²-4)(a²+4)
=4(a-2)(a+2)(a²+4)
x^4-18x²y²+81y^4
=(x²-9y²)²
=(x-3y)²(x+3y)²
(x²-y)²-(1-y)²
=(x²-y-1+y)(x²-y+1-y)
=(x²-1)(x²-2y+1)
=(x-1)(x+1)(x²-2y+1)
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