# Binomial Theorem Questions

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.

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

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.

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

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

and is the answer to the second question:

n = 9
a = -2?