Question

因式分解（有理数范围内） 1. x²y²-x²-y²-6xy+4 2. 4x²-6ax-18a² 3. 20a&s

因式分解（有理数范围内）
1.x⁴-1
2.x²+4x-xy-2y+4
3.4x²-12x+5
4.21x²-31x-22
5.4x²+4xy+y²-4x-2y-3
6.9x^5-35x³-4x
7.3x²-6x
8.49x²-25
9.6x²-13x+5
10.x²+2-3x
11.12x²-23x-24
12.(x+6)(x-6)-(x-6)
13.8x²-18
14.x²-(a-b)x-ab
15.x²+x+y²-y-2xy
16.若x-y=99,求x²+x+y²-y-2xy的值
17.9x⁴+35x²-4
18.x²-y²-2yz-z²

Answer 1

1.x²y²-4xy+4-(x²+y²+2xy)=(xy-2)²-(x+y)²=(xy-2-x-y)(xy-2+x+y)
2.(4x+6a)(x-3a)
3.abc(20a²-9ab-20b²）=abc(4a-5b)(5a+4b)
4.?
5.4x²(x+1)-25(x+1)=(4x²-25)(x+1)=(2x+5)(2x-5)(x+1)
6.(1-xy-y+x)(1-xy+y-x)=[x(1-y)+(1-y)][y(1-x)+(1-x)]=(x+1)(1-y)(y+1)(1-x)
7.m²(x²-1)-(x-1)=m²(x-1)(x+1)-(x-1)=(x-1)(m²x+m²-1)
8.(a-b)²-1=(a-b-1)(a-b+1)
9.(x-y)(y²-z²)=(x-y)(y-z)(y+z)

Answer 2

1. x²y²-x²-y²-6xy+4=[（xy)^2-4xy+4]-(x^2+y^2+2xy)=(xy-2)^2-(x+y)^2=(xy+x+y-2)(xy-x-y-2)

2. 4x²-6ax-18a²=2(2x+3)(x-3)

3. 20a³bc-9a²b²c-20ab³c=abc(20a^2-9ab-20b^2)=abc(4a-5b)(5a+4b)

4. 2ax-5x+2ax-5=(2ax-5)(x+1)

5. 4x³+4x²-25x-25=x(4x^2-25)+(4x^2-25)=(2x+5)(2x-5)(x+1)

6. (1-xy)²-(y-x)²=(1-xy+y-x)[1-xy-(y-x)]=(xy+x-y-1)(xy-x+y-1)

7. mx²-m²-x+1=m(x^2-1)-(x-1)=m(x+1)(x-1)-(x-1)=(x-1)(mx+m-1)

8. a²-2ab+b²-1=(a-b)^2-1=(a-b+1)(a-b-1)

9. y²(x-y)+z²(y-x)=y^2(x-y)-z^2(x-y)=(x-y)(y^2-z^2)=(x-y)(y+z)(y-z)

Answer 3

1. x²y²-x²-y²-6xy+4
=( x²y²-4xy+4)-(x²+2xy+y²)
=(xy-2)²-(x+y)²
=(xy-2+x+y)(xy-2-x-y)
2. 4x²-6ax-18a²
=(2x)²-6ax+(3/2a)²-(3/2a)²-18a²
=(2x-3/2a)²-(9/2a)²
=(2x-3/2a+9/2a)(2x-3/2a-9/2a)
=(2x+3a)(2x-6a)
=2(2x+3a)(x-3a)
3. 20a³bc-9a²b²c-20ab³c
=abc(20a²-9ab-20b²)
4. 2ax²-5x+2ax-5
=2a(x+1)-5(x+1)
=(x+1)(2a-5)
5. 4x³+4x²-25x-25
=4x²(x+1)-25(x+1)
=(x+1)(2x+5)(2x-5)
6. (1-xy)²-(y-x)²
=(1-xy+y-x)(1-xy-y+x)
=[(1-x)+y(1-x)][(1+x)-y(1+x)]
=(1-x)(1+y)(1+x)(1-y)
8. a²-2ab+b²-1
=(a-b)²-1
=(a-b+1)(a-b-1)
9. y²(x-y)+z²(y-x)
=(y²-z²)(x-y)
=(y-z)(y+z)(x-y)

Answer 4

x^2y^2-x^2-y^2-6xy+4=(xy-2)^2-(x+y)^2=(xy-2-x-y)(xy-2+x+y)

Answer 5

(xy+x+y-2)(xy-x-y-2)