Question

因式分解 急急急

1.（a+b)^2 -2a-2b+1
2.a(x-a)(y-a)-b(a-x)(y-a)
3.x^2 -y^2 +8x+4y+12
4.x^2-2x-120
5.x^2+5x-24
6.ab-a+b-1
7.8(x^2 -2y^2)-x(7x+y)+xy

Answer 1

(a+b)^2 -2a-2b+1
= (a+b)^2 -2(a+b)+1
= (a+b-1)^2

a(x-a)(y-a) -b(a-x)(y-a)
= a(x-a)(y-a) +b(x-a)(y-a)
= (x-a)(y-a)(a+b)

x^2 -y^2 +8x+4y+12
= x^2+8x+16 -y^2+4y-4
= (x+4)^2 -(y^2-4y+4)
= (x+4)^2 -(y-2)^2
= (x+4+y-2)(x+4-y+2)
= (x+y+2)(x-y+6)

x^2-2x-120
= (x-12)(x+10)

x^2+5x-24
= (x-3)(x+8)

ab-a+b-1
= a(b-1) +(b-1)
= (b-1)(a+1)

8(x^2 -2y^2)-x(7x+y)+xy
= 8x^2-16y^2 -7x^2-xy+xy
= x^2 -16y^2
= (x+4y)(x-4y)

　
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Answer 2

1.（a+b)^2 -2a-2b+1
=(a+b)^2-2(a+b)+1
=(a+b-1)^2
2.a(x-a)(y-a)-b(a-x)(y-a)
=a(x-a)(y-a)+b(x-a)(y-a)
=(x-a)(y-a)(a+b)
3.x^2 -y^2 +8x+4y+12
=(x+y)(x-y)+8x+4y+12
=(x+y+2)(x-y+6)
4.x^2-2x-120
=(x-12)(x+10)
5.x^2+5x-24
=(x+8)(x-3)
6.ab-a+b-1
=a(b-1)+(b-1)
=(b-1)(a+1)
7.8(x^2 -2y^2)-x(7x+y)+xy
=8x^2-16y^2-7x^2-xy+xy
=x^2-16y^2
=(x+4y)(x-4y)