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Counting & Binomials

Review question

Can we find the coefficient of $x^2$ in $(5 + 4x)(1 - x/2)^{10}$?
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Ref: R7078

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Question

Write down and simplify the first \(4\) terms in the expansion by the binomial theorem of \(\left(1 - \tfrac{1}{2}x\right)^{10}\).

Find the coefficient of \(x^2\) in the expansion of \[ (5 + 4x)\left(1 - \tfrac{1}{2}x\right)^{10}. \]