a) \(\left(x-3\right)\left(x-1\right)-3\left(x-3\right)\)
\(=\left(x-3\right)\left[\left(x-1\right)-3\right]\)
\(=\left(x-3\right)\left(x-4\right)\)
b) \(\left(x-1\right)\left(2x+1\right)+3\left(x-1\right)\left(x+2\right)\left(2x+1\right)\)
\(=\left(x-1\right)\left(2x+1\right)\left[1+3\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(2x+1\right)\left(1+3x+6\right)\)
\(=\left(x-1\right)\left(2x+1\right)\left(3x+7\right)\)
c) \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)
\(=3\left(2x+1\right)-\left(2x-5\right)\left(2x+1\right)\)
\(=\left(2x+1\right)\left(3-2x+5\right)\)
\(=\left(2x+1\right)\left(-2x+8\right)\)
d) \(\left(x-5\right)^2+\left(x-5\right)\left(x+5\right)-\left(5-x\right)\left(2x+1\right)\)
\(=\left(x-5\right)^2+\left(x-5\right)\left(x+5\right)+\left(x-5\right)\left(2x+1\right)\)
\(=\left(x-5\right)\left(x-5+x-5+2x+1\right)\)
\(=\left(x-5\right)\left(4x-11\right)\)
e) \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)