a/ \(\left(x^2-x+2\right)^2+\left(x-2\right)^2=\left(x^2-x+2\right)^2-x^2+x^2+\left(x-2\right)^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2\right)+2x^2-4x+4\)
\(=\left(x^2-2x+2\right)\left(x^2+2\right)+2\left(x^2-2x+2\right)\)
\(=\left(x^2-2x+2\right)\left(x^2+4\right)\)
b/ \(6x^5+15x^4+20x^3+15x^2+6x+1\)
\(=6x^5+6x^4+2x^3+9x^4+9x^3+3x^2+9x^3+9x^2+3x+3x^2+3x+1\)
\(=2x^3\left(3x^2+3x+1\right)+3x^2\left(3x^2+3x+1\right)+3x\left(3x^2+3x+1\right)+3x^2+3x+1\)
\(=\left(3x^2+3x+1\right)\left(2x^3+3x^2+3x+1\right)\)
\(=\left(3x^2+3x+1\right)\left(x^3+\left(x+1\right)^3\right)\)
\(=\left(3x^2+3x+1\right)\left(2x+1\right)\left(x^2-\left(x+1\right)x+\left(x+1\right)^2\right)\)
\(=\left(3x^2+3x+1\right)\left(3x+1\right)\left(x^2+x+1\right)\)
