Question

分解因式，急

1. 1/25 x^2-9y^2

2. x-xy^2

3 2mx^2-4mx+2m

4. (x^2+1)^2-(y^2+1)^2

5. a^4-2a^2+1

6. (a+2b)^2-a-2b

另附PO垂直OR，OQ垂直PR，其中点到直线的距离有几条

Answer 1

1. 1/25 x^2-9y^2=(1/5x+3y)(1/5x-3y)
2. x-xy^2=x(1-y²)=x(1+y)(1-y)
3 2mx^2-4mx+2m=2m(x²-2x+1)=2m(x-1)²
4. (x^2+1)^2-(y^2+1)^2=[(x²+1)+(y²+1)][(x²+1)-(y²+1)]=(x²+y²+2)(x²-y²)=(x²+y²+2)(x+y)(x-y)
5. a^4-2a^2+1=(a²-1)²=[(a+1)(a-1)]²=(a+1)²(a-1)²
6. (a+2b)^2-a-2b=(a+2b)²-(a+2b)=(a+2b)(a+2b-1)
点到直线的距离有5条

Answer 2

1. 1/25 x^2-9y^2=(1/5 x)^2-(3y)^2=(1/5 x-3y)(1/5 x+3y)
2. x-xy^2=x(1-y^2)=x(1-y)(1+y)
3. 2mx^2-4mx+2m=2m(x^2-2x+1)=2m(x-1)(x-1)
4. (x^2+1)^2-(y^2+1)^2=(x^2+1-y^2-1)(x^2+1+y^2+1)=(x^2-y^2)(x^2+y^2+2)=(x-y)(x+y)(x^2+y^2+2)
5. a^4-2a^2+1=(a^2-1)^2=(a-1)(a-1)(a+1)(a+1)
6. (a+2b)^2-a-2b=(a+2b)^2-(a+2b)=(a+2b)(a+2b-1)
如果PO与OR长度相等，那么只有两条，若不相等，则有三条。
希望这些答案对你有帮助

Answer 3

1. 1/25 x^2-9y^2
=(x/5-3y)(x/5+3y)

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

3 2mx^2-4mx+2m
=2m(x^2-2x+1)
=2m(x-1)^2

4. (x^2+1)^2-(y^2+1)^2
=(x^2+1+y^2+1)(x^2-1-y^2-1)
=(x^2+y^2+2)(x^2-y^2)
=(x^2+y^2+2)(x-y)(x+y)

5. a^4-2a^2+1
=(a^2-1)^2
=[(a-1)(a+1)]^2
=(a-1)^2(a+1)^2

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

另附PO垂直OR，OQ垂直PR，其中点到直线的距离有3条

Answer 4

1、题目略=（1/5x+3y）(1/5x-3y)
2、=x(1+y)(1-y)
3. =2m(x-1)^2
4. =(x^2+1+y^2+1)(x^2+1-y^2-1)=(x^2+y^2+2)(x+y)(x-y)
5 . =(a^2-1)^2=(a+1)^2*(a-1)^2
6. =(a+2b)(a+2b-1)

另附PO垂直OR，OQ垂直PR，其中点到直线的距离有几条
题意不清，不知所云

Answer 5

1.原式=(x/5+3y)(x/5-3y)
2.原式=x(1-y^2)=(1+y)(1-y)
3.原式=2m(x^2-2x+1)=2m(x-1)^2
4.原式=(x^2+1+y^2+1)(x^2+1-y^2-1)=(x^2+y^2+2)(x+y)(x-y)
5.原式=(a^2-1)^2=(a+1)^2(a-1)^2
6.原式=(a+2b)(a+2b-1)
3条PO、OQ、OR