Solution (source code)

= Solution

The <binomial theorem> gives coefficients $1,4,6,4,1$ for the fourth power. Substituting $2x$ for its variable gives
$$
\boxed{1+8x+24x^2+32x^3+16x^4=(1+2x)^4,\qquad a=1,\ b=2,\ m=4.}
$$