Find the coefficient of x in the expansion of (1 – 3x + 7x2)(1 – x)16. - Mathematics

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Sum

Find the coefficient of x in the expansion of (1 – 3x + 7x2)(1 – x)16.

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Solution

The given expression is (1 – 3x + 7x2)(1 – x)16.

= (1 – 3x + 7x2) [16C0(1)16(–x)0 + 16C1(1)15 (–x) + 16C2(1)14 (–x)2 + …]

= (1 – 3x + 7x2) (1 – 16x + 120x2 …)

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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Chapter 8: Binomial Theorem - Exercise [Page 142]

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NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 3 | Page 142

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