1.5ax+5bx+3ay+3by

Solution: =5x(a+b)+3y(a+b)

=(5x+3y)(a+b)

2.x^3-x^2+x- 1

Solution: = (x 3-x 2)+(x-1)

=x^2(x- 1)+ (x- 1)

=(x- 1)(x^2+ 1)

3.x2-x-y2-y

Solution: =(x2-y2)-(x+y)

=(x+y)(x-y)-(x+y)

=(x+y)(x-y- 1)

4、bc(b+c)+ca(c-a)-ab(a+b)

=bc(c-a+a+b)+ca(c-a)-ab(a+b)

= BC(c-a)+BC(a+b)+ca(c-a)-ab(a+b)

= BC(c-a)+ca(c-a)+BC(a+b)-ab(a+b)

=(bc+ca)(c-a)+(bc-ab)(a+b)

=c(c-a)(b+a)+b(a+b)(c-a)

=(c+b)(c-a)(a+b)。

5、x^2+3x-40

=(x+8)(x-5)。

6. (x 2+x+1) (x 2+x+2)-12, which can make y = x 2+x, then

The original formula =(y+ 1)(y+2)- 12.

=y^2+3y+2- 12=y^2+3y- 10

=(y+5)(y-2)

=(x^2+x+5)(x^2+x-2)

=(x^2+x+5)(x+2)(x- 1).

7、m +5n-mn-5m

m +5n-mn-5m= m -5m -mn+5n

= (m -5m )+(-mn+5n)

=m(m-5)-n(m-5)

=(m-5)(m-n)

8. Decomposition factor bc(b+c)+ca(c-a)-ab(a+b)

BC(b+c)+ca(c-a)-ab(a+b)= BC(c-a+a+b)+ca(c-a)-ab(a+b)

= BC(c-a)+ca(c-a)+BC(a+b)-ab(a+b)

=c(c-a)(b+a)+b(a+b)(c-a)

=(c+b)(c-a)(a+b)

9 、( ab+b)2？ (a+b)2

= (ab+b+a+b)(ab+b？ Answer? b)

= (ab+2b+a)(ab？ answer

= a(b？ 1)(ab+2b+a)。

10、3x^6-3x^2

=3x^2(x^4- 1)

=3x^2(x^2+ 1)(x^2- 1)

=3x^2(x^2+ 1)(x+ 1)(x- 1)