a) \(2x^2-x-6\)
\(=2x^2-4x+3x-6\)
\(=2x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(x-2\right)\left(2x+3\right)\)
b) \(4x^2+9x-9\)
\(=4x^2-3x+12x-9\)
\(=x\left(4x-3\right)+3\left(4x-3\right)\)
\(=\left(4x-3\right)\left(x+3\right)\)
c) \(2x^2-2x-12\)
\(=2x^2+4x-6x-12\)
\(=2x\left(x+2\right)-6\left(x+2\right)\)
\(=\left(x+2\right)\left(2x-6\right)\)
e) \(x^4y^4+64\)
\(=x^4y^4+16x^2y^2+64-16x^2y^2\)
\(=\left(x^2y^2\right)^2+2.8.x^2y^2+8^2-\left(4xy\right)^2\)
\(=\left(x^2y^2+8\right)^2-\left(4xy\right)^2\)
\(=\left(x^2y^2+8-4xy\right)\left(x^2y^2+8+4xy\right)\)
f) \(4x^4y^4+1\)
\(=\left(2x^2y^2\right)+4x^2y^2+1-4x^2y^2\)
\(=\left(2x^2y^2+1\right)^2-\left(2xy\right)^2\)
\(=\left(2x^2y^2+1-2xy\right)\left(2x^2y^2+1+2xy\right)\)
