a) Ta có: \(5x^2-10xy+5y^2-20z^2\)
\(=5\left(x^2-2xy+y^2-4z^2\right)\)
\(=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)
\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)
b) Ta có: \(x^2-8x+15\)
\(=x^2-3x-5x+15\)
\(=x\left(x-3\right)-5\left(x-3\right)\)
\(=\left(x-3\right)\left(x-5\right)\)
c) Ta có: \(2x^2-5xy+3y^2\)
\(=2x^2-2xy-3xy+3y^2\)
\(=2x\left(x-y\right)-3y\left(x-y\right)\)
\(=\left(x-y\right)\left(2x-3y\right)\)
d) Ta có: \(16y^3-2x^3-6x\left(x+1\right)-2\)
\(=16y^3-2x^3-6x^2-6x-2\)
\(=2\left[8y^3-x^3-3x^2-3x-1\right]\)
\(=2\left[\left(2y\right)^3-\left(x^3+3x^2+3x+1\right)\right]\)
\(=2\left[\left(2y\right)^3-\left(x+1\right)^3\right]\)
\(=2\left(2y-x-1\right)\left[\left(2y\right)^2+2y\left(x+1\right)+\left(x+1\right)^2\right]\)
\(=2\left(2y-x-1\right)\left(4y^2+2xy+2y+x^2+2x+1\right)\)