Question

Find the coefficient of x⁵ in the product (1 + 2x)⁶ (1 – x)⁷ using binomial theorem.

Answer 1

Using Binomial Theorem, the expressions, (1 + 2x)⁶ and (1 – x)⁷, can be expanded as

The complete multiplication of the two brackets is not required to be carried out. Only those terms, which involve x⁵, are required.

The terms containing x⁵ are

Thus, the coefficient of x⁵ in the given product is 171.