1: \(2a-2b=2\cdot a-2\cdot b=2\left(a-b\right)\)
2: \(2a+4b-6c\)
\(=2\cdot a+2\cdot2b-2\cdot3c\)
\(=2\left(a+2b-3c\right)\)
3: \(-4a-8b-12c\)
\(=-4\cdot a-4\cdot2b-4\cdot3c\)
\(=-4\left(a+2b+3c\right)\)
4: \(8xy-24y+16x\)
\(=8\cdot xy-8\cdot3y+8\cdot2x\)
\(=8\left(xy-3y+2x\right)\)
5: \(a-ax^2-ax-a\)
\(=-ax^2-ax\)
\(=-ax\left(x+1\right)\)
6: \(2ax-2ay+2a\)
\(=2a\cdot x-2a\cdot y+2a\cdot1\)
\(=2a\left(x-y+1\right)\)
7: \(5a-10ax-15ay\)
\(=5a\cdot1-5a\cdot2x-5a\cdot3y\)
\(=5a\left(1-2x-3y\right)\)
8: \(a\left(x-y\right)-b\left(x-y\right)\)
\(=\left(x-y\right)\left(a-b\right)\)
9: \(2a\left(x+y\right)-4\left(x+y\right)\)
\(=\left(x+y\right)\left(2a-4\right)\)
\(=\left(x+y\right)\left(2\cdot a-2\cdot2\right)\)
\(=2\left(x+y\right)\left(a-2\right)\)
10: \(5a^2\left(x-y\right)+10a\left(x-y\right)\)
\(=\left(x-y\right)\left(5a^2+10a\right)\)
\(=5a\left(a+2\right)\left(x-y\right)\)
11: \(3a\left(x-y\right)+2\left(x-y\right)\)
\(=3a\cdot\left(x-y\right)+2\cdot\left(x-y\right)\)
\(=\left(x-y\right)\left(3a+2\right)\)
12: mx(a+b)-m(a+b)
\(=\left(a+b\right)\left(mx-m\right)\)
\(=m\left(a+b\right)\left(x-1\right)\)
