Find the coefficient of x5 in ((1)/(p) + px)7.

Here are the solutions for problems 3 and 4.

: Binomial Expansion

Step 1: Find the coefficient of $x^5$ in $\left(\frac{1}{p} + px\right)^7$.
The general term in the binomial expansion of $(a+b)^n$ is $T_{r+1} = \binom{n}{r} a^{n-r} b^r$.
For $\left(\frac{1}{p} + px\right)^7$, we have $a = \frac{1}{p}$, $b = px$, and $n = 7$.
The general term is:

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