1.
\(14x^2y-21xy^2+28x^2y^2\)
\(=7xy\left(x-3y+4xy\right)\)
2.
\(5x\left(x-2\right)-3x^2\left(x-2\right)\)
\(=x\left(x-2\right)\left(5-3x\right)\)
3.
\(x^2\left(x-1\right)+2x\left(1-x\right)\)
\(=x^2\left(x-1\right)-2x\left(x-1\right)\)
\(=x\left(x-1\right)\left(x-2\right)\)
4.
\(3x\left(x-5y\right)-2y\left(5y-x\right)\)
\(=3x\left(x-5y\right)+2y\left(x-5y\right)\)
\(=\left(x-5y\right)\left(3x+2y\right)\)
5.
\(y^2\left(x^2+y\right)-zx^2-zy\)
\(=y^2\left(x^2+y\right)-z\left(x^2+y\right)\)
\(=\left(y^2-z\right)\left(x^2+y\right)\)
6.
\(b\left(a-c\right)+5c-5a\)
\(=b\left(a-c\right)-5\left(a-c\right)\)
\(=\left(b-5\right)\left(a-c\right)\)
7.
\(5\left(x+y\right)^2+15\left(x+y\right)\)
\(=5\left(x+y\right)\left(x+y+3\right)\)
8.
\(9x\left(x-y\right)-10\left(y-x\right)^2\)
\(=9x\left(x-y\right)-10\left(x-y\right)^2\)
\(=\left(x-y\right)\left(9x-10\left(x-y\right)\right)\)
\(=\left(x-y\right)\left(10y-x\right)\)
9.
\(7x\left(y-4\right)^2-\left(4-y\right)^3\)
\(=7x\left(y-4\right)^2+\left(y-4\right)^3\)
\(=\left(y-4\right)^2\left(7x-\left(y-4\right)\right)\)
\(=\left(y-4\right)^2\left(7x-y+4\right)\)
10.
\(\left(a-b\right)^2-\left(a+b\right)\left(b-a\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(a-b+a+b\right)\)
\(=2a\left(a-b\right)\)
11.
\(\left(x+1\right)\left(y-2\right)-\left(2-y\right)^2\)
\(=\left(x+1\right)\left(y-2\right)-\left(y-2\right)^2\)
\(=\left(y-2\right)\left(x+1-y+2\right)\)
\(=\left(y-2\right)\left(x-y+3\right)\)
12.
\(2x\left(x-3\right)+y\left(x-3\right)+3-x\)
\(=2x\left(x-3\right)+y\left(x-3\right)-\left(x-3\right)\)
\(=\left(x-3\right)\left(2x+y-1\right)\)
