1.\(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=\left(x^2+x\right)+2.2.\left(x^2+x\right)+4-16\)
\(=\left(x^2+x+1\right)-16=\left(x^2+x-3\right)\left(x^2+x+5\right)\)
2.\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left[\left(x+1\right)^2+3\left(x+1\right)\right]\left[x^2+5x+6\right]-24\)
\(=\left[\left(x+1\right)^2+3\left(x+1\right)\right]\left[\left(x+1\right)^2+3x+5\right]-24\)
\(=\left[\left(x+1\right)^2+3\left(x+1\right)\right]\left[\left(x+1\right)^2+3\left(x+1\right)+2\right]-24\)
\(=\left[\left(x+1\right)^2+3\left(x+1\right)\right]^2+2\left[\left(x+1\right)^2+3\left(x+1\right)\right]^2-24\)
\(=\left[\left(x+1\right)^2+3\left(x+1\right)+1\right]^2-25\)
\(=\left[\left(x+1\right)^2+3\left(x+1\right)-4\right]\left[\left(x+1\right)^2+3\left(x+1\right)+6\right]\)
\(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)
