2: \(x^2-xy+x-y\)
=x(x-y)+(x-y)
=(x-y)(x+1)
5: \(x^3-2x^2+x-2\)
\(=x^2\left(x-2\right)+\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+1\right)\)
8: \(xy+xz+3y+3z\)
\(=x\left(y+z\right)+3\left(y+z\right)\)
=(y+z)(x+3)
11: \(x^2+2x-xy-2y\)
\(=x\left(x+2\right)-y\left(x+2\right)\)
\(=\left(x+2\right)\left(x-y\right)\)
14: \(\left(x+1\right)\cdot y-2x-2\)
\(=y\left(x+1\right)-2\left(x+1\right)\)
=(x+1)(y-2)
17: \(x^2+xy-2x-2y\)
\(=x\left(x+y\right)-2\left(x+y\right)\)
=(x+y)(x-2)
20: \(3x^2-3xy-5x+5y\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
23: \(3x^2-2x-3xy+2y\)
\(=x\left(3x-2\right)-y\left(3x-2\right)\)
=(3x-2)(x-y)
26: \(9x^3-9x^2y-4x+4y\)
\(=9x^2\left(x-y\right)-4\left(x-y\right)\)
\(=\left(x-y\right)\left(9x^2-4\right)=\left(x-y\right)\left(3x-2\right)\left(3x+2\right)\)
29: \(x^3+2x^2-4x-8\)
\(=x^2\left(x+2\right)-4\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-4\right)=\left(x+2\right)^2\cdot\left(x-2\right)\)
32: \(10ax-5ay-2x+y\)
\(=5a\left(2x-y\right)-\left(2x-y\right)\)
\(=\left(2x-y\right)\left(5a-1\right)\)
35: ax-bx+ab-x2
\(=ax-x^2-bx+ab\)
\(=x\left(a-x\right)-b\left(x-a\right)\)
\(=x\left(a-x\right)+b\left(a-x\right)=\left(a-x\right)\left(x+b\right)\)
3: \(xy+y^2-x-y\)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(y-1\right)\)
6: \(x^4+x^3y-x-y\)
\(=x^3\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^3-1\right)=\left(x+y\right)\left(x-1\right)\left(x^2+x+1\right)\)
9: \(x^2-3x+xy-3y\)
\(=x\left(x-3\right)+y\left(x-3\right)\)
=(x-3)(x+y)
12: \(3x^2-x-3xy+y\)
\(=x\left(3x-1\right)-y\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x-y\right)\)
15: \(x^2-2xy+x-2y\)
=x(x-2y)+(x-2y)
=(x-2y)(x+1)
18: \(x^2-xy-6x+6y\)
\(=x\left(x-y\right)-6\left(x-y\right)\)
\(=\left(x-y\right)\left(x-6\right)\)
24:\(3x^2-3xy-5x+5y\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
21: \(x^2-6x-2xy+12y\)
\(=x\left(x-6\right)-2y\left(x-6\right)\)
\(=\left(x-6\right)\left(x-2y\right)\)
27: \(2x^2-6xy+5x-15y\)
\(=2x\left(x-3y\right)+5\left(x-3y\right)\)
=(x-3y)(2x+5)
30: \(5xy^2-5x+y^2-1\)
\(=5x\left(y^2-1\right)+\left(y^2-1\right)\)
\(=\left(5x+1\right)\left(y^2-1\right)=\left(5x+1\right)\left(y-1\right)\left(y+1\right)\)
38: \(a^3-a^2x-ay+xy\)
\(=a^2\left(a-x\right)-y\left(a-x\right)\)
\(=\left(a-x\right)\left(a^2-y\right)\)
