a: \(16x^4\left(x-y\right)-x+y\)
\(=16x^4\left(x-y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(16x^4-1\right)=\left(x-y\right)\left(4x^2+1\right)\left(4x^2-1\right)\)
\(=\left(x-y\right)\left(4x^2+1\right)\left(2x-1\right)\left(2x+1\right)\)
c: \(16x^3-54y^3=2\left(8x^3-27y^3\right)\)
\(=2\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)\)
e: \(x^2-9+\left(2x+7\right)\left(3-x\right)\)
\(=\left(x-3\right)\left(x+3\right)-\left(2x+7\right)\cdot\left(x-3\right)\)
\(=\left(x-3\right)\left(x+3-2x-7\right)=\left(-x-4\right)\left(x-3\right)\)
g: \(4x^3-4x^2-x+1\)
\(=4x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(4x^2-1\right)=\left(x-1\right)\left(2x-1\right)\left(2x+1\right)\)
b: \(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\cdot x^2-2xy\cdot y^2-2xy\cdot2y-2xy\cdot1\)
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
d: \(x^3+x^2-4x-4\)
\(=x^2\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-4\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
f: \(x^2-2x+1-4y^2\)
\(=\left(x^2-2x+1\right)-4y^2\)
\(=\left(x-1\right)^2-\left(2y\right)^2=\left(x-1-2y\right)\left(x-1+2y\right)\)
h: \(x^4-4x^3+4x^2=x^2\cdot x^2-x^2\cdot4x+x^2\cdot4\)
\(=x^2\cdot\left(x^2-4x+4\right)=x^2\left(x-2\right)^2\)
