a: \(x^3y^2+10x^2y^2+25xy^2\)
\(=xy^2\left(x^2+10x+25\right)\)
\(=xy^2\left(x+5\right)^2\)
b: \(4x^2-4y^2+4y-1\)
\(=4x^2-\left(4y^2-4y+1\right)\)
\(=4x^2-\left(2y-1\right)^2\)
\(=\left(2x-2y+1\right)\left(2x+2y-1\right)\)
c: \(45+x^3-5x^2-9x\)
\(=\left(x^3-5x^2\right)-9\left(x-5\right)\)
\(=x^2\left(x-5\right)-9\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2-9\right)=\left(x-5\right)\left(x-3\right)\left(x+3\right)\)
d: \(\left(x^2+2x\right)\left(x^2+2x-2\right)-3\)
\(=\left(x^2+2x\right)^2-2\left(x^2+2x\right)-3\)
\(=\left(x^2+2x-3\right)\left(x^2+2x+1\right)\)
\(=\left(x+3\right)\cdot\left(x-1\right)\cdot\left(x+1\right)^2\)
