a: \(x^2-4x-25y^2+4\)
\(=\left(x^2-4x+4\right)-\left(5y\right)^2\)
\(=\left(x-2\right)^2-\left(5y\right)^2=\left(x-2-5y\right)\left(x-2+5y\right)\)
b: \(x^2-3x+xy-3y\)
=x(x-3)+y(x-3)
=(x-3)(x+y)
c: \(3x^2+6xy+3y^2-3z^2\)
\(=3\left(x^2+2xy+y^2-z^2\right)\)
\(=3\left\lbrack\left(x+y\right)^2-z^2\right\rbrack\)
=3(x+y+z)(x+y-z)
d: \(2x^2-5x+2\)
\(=2x^2-4x-x+2\)
=2x(x-2)-(x-2)
=(x-2)(2x-1)
e: \(\left(2x+y\right)^2-4x^2+12x-9\)
\(=\left(2x+y\right)^2-\left(4x^2-12x+9\right)=\left(2x+y\right)^2-\left(2x-3\right)^2\)
=(2x+y+2x-3)(2x+y-2x+3)
=(4x+y-3)(y+3)
f: \(a^3-1+5a^2-5+3a-3\)
\(=\left(a-1\right)\left(a^2+a+1\right)+5\left(a^2-1\right)+3\left(a-1\right)\)
=(a-1)(a^2+a+1)+5(a-1)(a+1)+3(a-1)
=(a-1)[a^2+a+1+5a+5+3]
=(a-1)(a^2+6a+9)
=(a-1)(a+3)^2
