大师作文网因式分解 (a方+b方-1)方-4a方b方
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/17 05:00:32
因式分解 (a方+b方-1)方-4a方b方
1.（x方-x）方-14（x方-x）+24
2.（x方-5x）（x方-5x-2）-24
3.（x-y）n次方-（x-y）n-3次方
4.（1-a方）（1-b方）-4ab
1.（x方-x）方-14（x方-x）+24
2.（x方-5x）（x方-5x-2）-24
3.（x-y）n次方-（x-y）n-3次方
4.（1-a方）（1-b方）-4ab
(a方+b方-1)方-4a方b方=a^4+b^4-2a^2b^2-2(a^2+b^2)+1
=(a^2-b^2)^2-2(a^2-b^2)+1-4b^2
=(a^2-b^2-1-2b)(a2-b^2-1+2b)
=(a-b-1)(a+b+1)(a-b+1)(a+b-1)
(x方-x)方-14(x方-x)+24=(x^2-x-2)(x^2-x-12)
=(x-2)(x+1)(x-4)(x+3)
(x方-5x)(x方-5x-2)-24=(x^2-5x)^2-2(x^2-5x)-24
=(x^2-5x-6)(x^2-5x+4)
=(x-6)(x+1)(x-1)(x-4)
(x-y)^n-(x-y)^(n-3)=[(x-y)^(n-3)][(x-y)^3-1]
=[(x-y)^(n-3)](x-y-1)[(x-y)^2+(x-y)+1]
(1-a^2)(1-b^2)-4ab=1-a^2-b^2+a^2*b^2-4ab
=(ab)^2-2ab-2ab-a^2-b^2+1
=(ab-1)^2-(a+b)^2
=(ab-a-b-1)(ab+a+b-1)
=(a^2-b^2)^2-2(a^2-b^2)+1-4b^2
=(a^2-b^2-1-2b)(a2-b^2-1+2b)
=(a-b-1)(a+b+1)(a-b+1)(a+b-1)
(x方-x)方-14(x方-x)+24=(x^2-x-2)(x^2-x-12)
=(x-2)(x+1)(x-4)(x+3)
(x方-5x)(x方-5x-2)-24=(x^2-5x)^2-2(x^2-5x)-24
=(x^2-5x-6)(x^2-5x+4)
=(x-6)(x+1)(x-1)(x-4)
(x-y)^n-(x-y)^(n-3)=[(x-y)^(n-3)][(x-y)^3-1]
=[(x-y)^(n-3)](x-y-1)[(x-y)^2+(x-y)+1]
(1-a^2)(1-b^2)-4ab=1-a^2-b^2+a^2*b^2-4ab
=(ab)^2-2ab-2ab-a^2-b^2+1
=(ab-1)^2-(a+b)^2
=(ab-a-b-1)(ab+a+b-1)