a: \(25-y^2-4x^2-4xy\)
\(=25-\left(4x^2+4xy+y^2\right)\)
\(=5^2-\left(2x+y\right)^2\)
\(=\left(5-2x-y\right)\left(5+2x+y\right)\)
b: \(2x^2-8xy+8y^2-2z^2-8x^2+8z\)
\(=2\left(x^2-4xy+4y^2-z^2-4x^2+4z\right)\)
\(=2\left(-3x^2-4xy+4y^2-z^2+4z\right)\)
d: \(x^5-x^4+x^3-x^2\)
\(=x^4\left(x-1\right)+x^2\left(x-1\right)\)
\(=\left(x-1\right)\left(x^4+x^2\right)=x^2\left(x^2+1\right)\left(x-1\right)\)
e: \(x^4+64\)
\(=x^4+16x^2+64-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
f: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24-24\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)\)
\(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)
\(=x\left(x+5\right)\left(x^2+5x+10\right)\)
