Question

因式分解 要过程

1. 4x^2-a^2-6a-9
2. 3a^2-6ab+3b^3-5a+5b
3. a^2-b^2-c^2+d^2-2(ad-bc)
4.16-x^2n-100+20x^n
5. x^3-x^2-x-y^3+y^2+y

Answer 1

1. 4x^2-a^2-6a-9
=4x²-(a²+6a+9)
=(2x)²-(a+3)²
=(2x+a+3)(2x-a-3)

2. 3a^2-6ab+3b^3-5a+5b
=3(a²-2ab+b²)-5(a-b)
=3(a-b)²-5(a-b)
=(a-b)(3a-3b-5)

3. a^2-b^2-c^2+d^2-2(ad-bc)
=a²-2ad+d²-b²+2bc-c²
=(a-d)²-(b-c)²
=(a-d+b-c)(a-d-b+c)

4.16-x^2n-100+20x^n
=4²-(x^2n-20x^n+10²)
=4²-(x^n-10)²
=(4+x^n-10)(4-x^n+10)
=(x^n-6)(14-x^n)

5. x^3-x^2-x-y^3+y^2+y
=x^3-y^3-x^2+y^2-x+y
=(x-y)(x²+xy+y²)-(x-y)(x+y)-(x-y)
=(x-y)(x²+xy+y²-x-y-1)

Answer 2

. x^3-x^2-x-y^3+y^2+y

=. x^3-y^3+y^2-x^2+y-x
=(x-y)(x^2+xy+y^2)+(y-x)(y+x)+(y-x)
=(y-x)(y+x-x^2-xy-y^2+1)

追问

肿么就一个捏。