Question

因式分解 要有过程 谢谢

1 15x^2-15x-2xy+2y
2 a^3+a^2b+a^2c+abc
3 2ab-a^2-b^2+c^2
4 x^2-4xy+4y^2-2x+4y+1
5 x^2-6xy+9y^2-1

Answer 1

1 15x^2-15x-2xy+2y
＝15x(x-1)-2y(x-1)
=(15x-2y)(x-1)

2 a^3+a^2b+a^2c+abc
=a^2b(a+b)+ac(a+b)
=a(ab+c)(a+b)

3 2ab-a^2-b^2+c^2
=c^2-(a-b)^2
=(c+a-b)(c-a+b)

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

5 x^2-6xy+9y^2-1
=(x-3y)^2-1
=(x-3y+1)(x-3y-1)

Answer 2

答案如下：1 15x^2-15x-2xy+2y
＝15x(x-1)-2y(x-1)
=(15x-2y)(x-1)

2 a^3+a^2b+a^2c+abc
=a^2b(a+b)+ac(a+b)
=a(ab+c)(a+b)

3 2ab-a^2-b^2+c^2
=c^2-(a-b)^2
=(c+a-b)(c-a+b)

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

5 x^2-6xy+9y^2-1
=(x-3y)^2-1
=(x-3y+1)(x-3y-1)

Answer 3

1、=15x（x-1）-2y(x-1)
=（x-1）(15-2y)
2、=a^2(a+b)+ac(a+b)
=a(a+b)(a+c)
3、=c^2-(a^2-2ab+b^2)
=c^2-(a-b)^2
=(c-a+b)(c+a-b)
4、=（x-2y）^2-2(x-2y)+1
=(x-2y)(x-2y-1)
5、=（x-3y）^2-1
=(x-3y-1)(x-3y+1)