# Thread: Binomial Theorem or Binomial Coefficient

1. ## Binomial Theorem or Binomial Coefficient

I hope this is the right part of the forum for this question.

In the expansion of (1+ax)^4, the coefficient of x^3 is 1372. Find the constant a.

2. $(1+ax)^4 = \sum_{n=1}^{4} \binom{4}{n}a^nx^n$

So the coefficient of x^3 is $\binom{4}{3}a^3$

Can you solve this now?

3. By the binomial expansion, $4a^{3}=1372$.

Solve for a.

Understand the pattern. $a^{4}x^{4}+4a^{3}x^{3}+6a^{2}x^{2}+4ax+1$

4. Thanks, i got it now, i had to equate the 4C3 part of the expansion to 1372x^3

Thanks