# Binomial Theorem Questions

1. Nov 30, 2004

### nobb

Hey.
I am having difficultly with two math problems:

1. In the expansion of (mx+n)^5 the numerical coefficient of the second term is -48 and of the third term if 28.8 Find the values of m and n.

2. The first three terms in the expansion of (1+a)^n are 1-18+144. Determine the values of a and n

Could someone please explain to me how to do these? Thanks.

Last edited: Nov 30, 2004
2. Nov 30, 2004

### Sirus

Consider that:
$$(a+b)^{n}=\sum_{r=0}^{n}{\left(\begin{array}{1}n\\r\end{array}\right)}a^{n-r}b^r$$

3. Nov 30, 2004

### nobb

I've expanded it so that term two is equal to 5(m^4)(x^4)n. Term three is equal to 5(m^3)(x^3)(n^2). Now I am stuck and I do not know what to do with the coefficients.

4. Nov 30, 2004

### Justin Lazear

Your third term is not correct.

Once you have the terms, you simply set the second term equal to the value you were given for the second term, and set the third term equal to the value you were given for the third term. This gives you a system of two equations in two variables, so you may solve it.

Your second problem works exactly the same way.

--J

5. Nov 30, 2009

### sweet777

is the answer to the first question:
m = 2
n = -0.6

and is the answer to the second question:

n = 9
a = -2?