Question

simplify 729m^3+243m^2+27m+1​

Answer 1

We know 729m³ is a cube of 9m. 1 is a cube of itself.

The suitable identity here is $(a+b)^3=a^3+b^3+3ab(a+b)$. Here a=9m, b=1.

$(9m)^3+(1)^3+27m(9m+1)$ is correct. Now we simplify using this one.

The answer is clearly $(9m+1)^3$.