a) Ta có: \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)-384\)
\(=\left[\left(x+1\right)\left(x+7\right)\right]\left[\left(x+3\right)\left(x+5\right)\right]-384\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)-384\)
\(=\left(x^2+8x\right)^2+22\left(x^2+8x\right)+105-384\)
\(=\left(x^2+8x\right)^2+22\left(x^2+8x\right)-279\)
\(=\left(x^2+8x\right)^2+31\left(x^2+8x\right)-9\left(x^2+8x\right)-279\)
\(=\left(x^2+8x\right)\left(x^2+8x+31\right)-9\left(x^2+8x+31\right)\)
\(=\left(x^2+8x+31\right)\left(x^2+8x-9\right)\)
\(=\left(x^2+8x+31\right)\left(x+9\right)\left(x-1\right)\)
