Binomial Theorem

We can use the binomial theorem to find the coefficient of the term $x^3$ in the expansion of $(1 + ax)^n$.

The binomial theorem states that, for any real number a and any positive integer n, the expansion of (1 + ax)^n is given by:

$(1 + ax)^n = C(n, 0) * 1^(n-0) * (ax)^0 + C(n, 1) * 1^(n-1) * (ax)^1 + C(n, 2) * 1^(n-2) * (ax)^2 + ... + C(n, n) * 1^(n-n) * (ax)^n$

where C(n, k) is the binomial coefficient given by:

$C(n, k) = n! / (k! (n-k)!)$

where n! means n factorial, $i.e., n! = n * (n-1) * (n-2) * ... * 1$.

So, to find the coefficient of x^3 in the expansion of $(1 + ax)^n$, we need to find $C(n, 3) * 1^(n-3) * (ax)^3$.

Since $1^(n-3) = 1$, the coefficient of $x^3$ is simply $C(n, 3) * ax^3 = n! / (3! (n-3)!) * a^3$.

Therefore, if c is the coefficient of $x^3$ in the expansion of $(1 + ax)^n$, we have:

$c = n! / (3! (n-3)!) * a^3$

So, to find c, we need the values of n and a. Unfortunately, the problem doesn't give us these values, so we cannot find c without more information.