Find out the sum of the coefficients in the expansion of the binomial ${(5 p - 4 q)}^{n}$ where $n \in N$

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Solution

Consider the above expression
$(5 p - 4 q)^{n}$ .
For finding the sum of the coefficients, we substitute $p = q = 1$
Then the sum of the coefficients becomes
$(5 p - 4 q)_{p = q = 1}^{n}$
$= (5 - 4)^{n}$
$= 1^{n}$
$= 1$ .

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