Question

find the term x^4 in the expansion ((x/2)-3)^7

Answer 1

\[\large
\left(\frac x2 - 3\right)^7 =
\sum_{k = 0}^{7}\binom{7}{k}\left( \frac x2\right)^{7-k}(-3)^k \normalsize ~~~~
\text{-------(1)} \\
\text{ } \\
x^4 \text{ occurs when } k = 3. \\
\text{ } \\
\text{Put k = 3 in (1) and evaluate: }
\binom{7}{k}\left( \frac x2\right)^{7-k}(-3)^k
\]