7年级奥数——因式分解（要有过程）

Question

1.5a(m-n)-10a(m-n)
2.(x+y)²（x-y）+（x+y）（x-y）²
3.x²y²-0.04
4.-m²+1/16
5.9a²-12a+4
6.4x²+20xy+25y²
7.x²+7x+12
8.x²-4xy-96y²

Answer 1

1.5a(m-n)-10a(m-n)
=-5a(m-n)
2.(x+y)²（x-y）+（x+y）（x-y）²
=(x+y)(x-y)(x+y+x-y)
=2x(x+y)(x-y)
3.x²y²-0.04
=(xy+0.2)(xy-0.2) (平方差）
4.-m²+1/16
=-(m+1/4)(m-1/4) (平方差）
5.9a²-12a+4
=(3a-2)^2 (完全平方）
6.4x²+20xy+25y²
=（2x+5y)^2 (完全平方）

7.x²+7x+12
=(x+3)(x+4) (交叉相乘）
8.x²-4xy-96y²
=（x+8y)(x-12y) (交叉相乘）

Answer 2

1.5a(m-n)-10a(m-n)
=5a(m-n)(1-2)
=-5a(m-n)

2.(x+y)²（x-y）+（x+y）（x-y）²
=(x+y)(x-y)(x+y+x-y)
=2x(x+y)(x-y)

3.x²y²-0.04
=(xy-0.2)(xy+0.2)

4.-m²+1/16
=1/16-m^2
=(1/4-m)(1/4+m)

5.9a²-12a+4
=(3a-2)^2

6.4x²+20xy+25y²
=(2x+5y)^2

7.x²+7x+12
=(x+3)(x+4)

8.x²-4xy-96y²
=(x-12)(x+8)

Answer 3

1.-5a(m-n)
2.2x(x+y)（x-y）
3.(xy+0.2)(xy-0.2)
4.(-m+1/4)(m-1/4)
5.(3a-2)²
6.(2x+5y)²
7.(x+4)(x+3)
8.(x+8y)(x-12y)

Answer 4

1. 5a(m-n)-10a(m-n)=（m-n）*a*（5-10）=-5a（m-n）
2. (x+y)²(x-y)+（x+y)(x-y）²=（x+y)(x+y)(x-y）+（x+y)(x-y)(x-y）
=(x+y)(x-y)(x+y+x-y)=2x(x+y)(x-y)
3. x²y²-0.04=(xy)²-0.2²=(xy+0.2)(xy-0.2)
4. -m²+1/16=1/16-m²=(1/4)²-m²=(1/4+m)(1/4-m)
5. 9a²-12a+4=(3a)²-2*2*3a+2²=(3a-2)²
6. 4x²+20xy+25y²=(2x)²+2*2x*5y+(5y)²
7. x²+7x+12=x²+(3+4)x+3*4=(x+3)*(x+4)
8. x²-4xy-96y²=x²+x*(-12y+8y)-12y*8y=(x-12y)(x+8y)