a) \(3x^2y-6xy^2\)
\(=3xy\left(x-2y\right)\)
b) \(25x^2-y^2\)
\(=\left(5x\right)^2-y^2\)
\(=\left(5x-y\right)\left(5x+y\right)\)
c) \(4a^2-4a+1\)
\(=\left(2a\right)^2-2.2a+1\)
\(=\left(2a-1\right)^2\)
d) \(125-a^3\)
\(=5^3-a^3\)
\(=\left(5-a\right)\left(25+5a+a^2\right)\)
e) \(7\left(a+b\right)-14\left(a+b\right)\)
\(=7\left(a+b\right)\left(1-2\right)\)
\(=-7\left(a+b\right)\)
f) \(13\left(x-y\right)+36a\left(y-x\right)\)
\(=13\left(x-y\right)-36a\left(x-y\right)\)
\(=\left(x-y\right)\left(13-36a\right)\)
g) \(3x-3y+7xy-7x^2\)
\(=3\left(x-y\right)+7x\left(y-x\right)\)
\(=3\left(x-y\right)-7x\left(x-y\right)\)
\(=\left(x-y\right)\left(3-7x\right)\)
h) \(5x^2+5y^2-20z^2-10xy\)
\(=5\left(x^2+y^2-4z^2-2xy\right)\)
\(=5\left[\left(x^2-2xy+y^2\right)-\left(2z\right)^2\right]\)
\(=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)
\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)
