multiply the following polynomials.

4a(a^2+7a+4)

4a(a^2+7a+4)

= 4a(a^2) + 4a(7a) + 4a(4) (Distributive property)

= 4a^3 + 28a^2 + 16a (Simplify)

Therefore, 4a(a^2+7a+4) = 4a^3 + 28a^2 + 16a.