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Sum

Find the coefficient of x in the expansion of (1 – 3x + 7x^{2})(1 – x)^{16}.

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#### Solution

The given expression is (1 – 3x + 7x^{2})(1 – x)^{16}.

= (1 – 3x + 7x^{2}) [^{16}C_{0}(1)^{16}(–x)^{0} + ^{16}C_{1}(1)^{15} (–x) + ^{16}C_{2}(1)^{14} (–x)^{2} + …]

= (1 – 3x + 7x^{2}) (1 – 16x + 120x^{2} …)

Collecting the term containing x

We get –16x – 3x = – 19x

Hence, the coefficient of x = –19

Concept: Binomial Theorem for Positive Integral Indices

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