UC知道因式分解一堆
来源：百度知道 编辑：UC知道 时间：2024/05/26 17:24:11
1.a^4+a^2b^2+b^4
2.x^4-11x^2+1
3.x^4-4x+3
4.a^4+2a^3b+3a^2b^2+2ab^3+b^4
5.a^2+2ab-ac-3b^3+5bc-2c^2
2.x^4-11x^2+1
3.x^4-4x+3
4.a^4+2a^3b+3a^2b^2+2ab^3+b^4
5.a^2+2ab-ac-3b^3+5bc-2c^2
1.a^4+a^2b^2+b^4
=(a^2)^2+2a^2b^2+(b^2)^2-a^2b^2
=(a^2+b^2)^2-a^2b^2
=(a^2+b^2)^2-(ab)^2
=(a^2+b^2+ab)(a^2+b^2-ab)
2.x^4-11x^2+1
=x^2(x^2-11+1/x^2)
=x^2*[(x-1/x)^2-9]
=x^2(x-1/x+3)(x-1/x-3)
=(x^2+3x-1)(x^2-3x-1)
3.x^4-4x+3 = (x-1)(x³+x²+x-3)=(x-1)²(x²+2x+3)
4.a^4+2a^3b+3a^2b^2+2ab^3+b^4
=(a^4+b^4+a^2b^2)+2ab(a^2+ab+b^2)
=[(a^2+b^2)^2-a^2b^2]+2ab(a^2+ab+b^2)
=(a^2+ab+b^2)(a^2-ab+b^2)+)+2ab(a^2+ab+b^2)
=(a^2+ab+b^2)^2
5.