\(x^3+12x^2+48x+64\)
= \(\left(x^3+64\right)+\left(12x^2+48x\right)\)
= \(\left(x+4\right)\left(x^2-4x+16\right)+12x\left(x+4\right)\)
= \(\left(x+4\right)\left(x^2-4x+16+12x\right)\)
= \(\left(x+4\right)\left(x^2-8x+16\right)\)
= \(\left(x+4\right)\left(x-4\right)^2\)