Question

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

Answer 1

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