\(a,x^2+4xy+4y^2-4\left(x+2y\right)+3\\ =\left(x^2+4xy+4y^2\right)-4\left(x+2y\right)+3\\ =\left(x+2y\right)^2-4\left(x+2y\right)+3\\ =\left[\left(x+2y\right)^2-\left(x+2y\right)\right]+\left[-3\left(x+2y\right)+3\right]\\ =\left(x+2y\right)\left(x+2y-1\right)-3\left(x+2y-1\right)\\ =\left(x+2y-1\right)\left(x+2y-3\right)\\ b,x\left(x+1\right)\left(x+2\right)\left(x+3\right)-3\\ =\left[x\left(x+3\right)\right]\left[\left(x+1\right)\left(x+2\right)\right]-3\\ =\left(x^2+3x\right)\left(x^2+3x+2\right)-3\\ =\left[\left(x^2+3x+1\right)-1\right]\left[\left(x^2+3x+1\right)+1\right]-3\\ =\left(x^2+3x+1\right)^2-1-3\\ =\left(x^2+3x+1\right)^2-4\\ =\left(x^2+3x+1-2\right)\left(x^2+3x+1+2\right)\\ =\left(x^2+3x-1\right)\left(x^2+3x+3\right)\)