a) \(2xy^3-6x^2+10xy=2xy\left(y^2-3x+5\right)\)
c: \(x^2-2xy+y^2-25=\left(x+y-5\right)\left(x+y+5\right)\)
e: \(125-x^6=\left(5-x^2\right)\left(x^4+5x^2+25\right)\)
g: \(a^2+2ab+b^2-ac-bc=\left(a+b\right)\left(a+b-c\right)\)
e: \(x^2+8x+15=\left(x+3\right)\left(x+5\right)\)
k: \(x^2+4x+3=\left(x+1\right)\left(x+3\right)\)
b: \(x^3-3x^2+3x-1-y^3\)
\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+y\left(x-1\right)+y^2\right]\)
d: \(a^6-a^5-2a^3+2a^2\)
\(=a^5\left(a-1\right)-2a^2\left(a-1\right)\)
\(=a^2\left(a-1\right)\left(a^3-2\right)\)
f: \(4x^4+4x^2y^2-8y^4\)
\(=4\left(x^4+x^2y^2-2y^4\right)\)
\(=4\left(x^4+2x^2y^2-x^2y^2-2y^4\right)\)
\(=4\cdot\left[x^2\left(x^2+2y^2\right)-y^2\left(x^2+2y^2\right)\right]\)
\(=4\left(x^2+2y^2\right)\left(x-y\right)\left(x+y\right)\)
h: \(x^2\left(x-1\right)+16\left(1-x\right)\)
\(=x^2\left(x-1\right)-16\left(x-1\right)\)
\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
j: \(x^2-x-12\)
\(=x^2-4x+3x-12\)
\(=\left(x-4\right)\left(x+3\right)\)
l: \(4x^2+4x-3\)
\(=4x^2+6x-2x-3\)
\(=2x\left(2x+3\right)-\left(2x+3\right)\)
\(=\left(2x+3\right)\left(2x-1\right)\)
