First expand each polynomial according to its exponent.
You then expand the results gotten for each expanded polynomial and multiply the two term by term to get the required expansion.
For example:
(a + b)^3(c + d) ^2 = (a^3 + 3a^2b + 3ab^2 + b^3)(c^2 + 2cd + d^2)
= a^3(c^2 + 2cd + d^2) + 3a^2b(c^2 + 2cd + d^2) + 3ab^2(c^2 + 2cd + d^2) + b^3(c^2 + 2cd + d^2)
From here, remove the brackets and simplify your answers where possible.