a.2x2-12x2+18x
=>2x(x2-6x+9)
=>2x(x-3)2
b.(x2+x)2+4x2+4x-12
=>x4+2x3+x2+4x2+4x-12
=>x4+2x3+5x2+4x-12
a) \(2x^3-12x^2+18x=2x\left(x^2+6x+9\right)=2x\left(x+3\right)^2\)
b) \(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
\(=\left(x^2+x\right)^2+6\left(x^2+x\right)-2\left(x^2+x\right)-12\)
\(=\left(x^2+x\right)\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x-2\right)\left(x^2+x+6\right)\)
\(=\left(x^2-x+2x-2\right)\left(x^2+x+6\right)\)
\(=\left[x\left(x-1\right)+2\left(x-1\right)\right]\left(x^2+x+6\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
