a) \(\left(x+2\right)^2=x^2+4x+4\)
b) \(\left(x-4y\right)\left(x+4y\right)=x^2-\left(4y\right)^2=x^2-16y^2\)
c) \(\left(2x-3y\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot\left(3y\right)+3\cdot\left(2x\right)\cdot\left(3y\right)^2-\left(3y\right)^3\)
\(=8x^3-36x^2y+1587xy^2-27y^3\)
d) \(\left(x-3\right)\left(x^2+3x+9\right)=x^3-3^3=x^3-27\)