a) \(x^4-4x^3+8x^2-16x+16\)
\(=x^4-2x^3-2x^3+4x^2+4x^2-8x-8x+16\)
\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3-2x^2+4x-8\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\)
\(=\left(x-2\right)\left(x-2\right)\left(x^2+4\right)\)
\(=\left(x-2\right)^2\left(x^2+4\right)\)
b) \(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)
c/ \(a^2+2ab+b^2-ac-bc\)
\(=\left(a+b\right)^2-c\left(a+b\right)\)
\(=\left(a+b\right)\left(a+b-c\right)\)
d/ \(ac-bc-a^2+2ab-b^2\)
\(=c\left(a-b\right)-\left(a^2-2ab+b^2\right)\)
\(=c\left(a-b\right)-\left(a-b\right)^2\)
\(=\left(a-b\right)\left(c-a+b\right)\)
e/ \(\left(x-y+5\right)^2-2\left(x-y+5\right)+1\)
\(=\left(x-y+5\right)\left(x-y+5-2\right)+1\)
\(=\left(x-y+5\right)\left(x-y+3\right)+1\)
f/ \(2x^2+7x+5\)
\(=2x^2+2x+5x+5\)
\(=2x\left(x+1\right)+5\left(x+1\right)\)
\(=\left(x+1\right)\left(2x+5\right)\)