Find the coefficient of x^4 in the expansion of (x + 1/x)^12.

Find the coefficient of $x^{4}$ in the expansion of $(x + \frac{1}{x})^{12}$ .

hard 3 marks Class 11 · Mathematics · Binomial Theorem

Answer

495

The correct answer is 495 — Thus the coefficient of $x^{4}$ is $495$ .

Write the general term: $T_{k+1} = \binom{12}{k}x^kleft(\frac{1}{x}\right)^{12-k} = \binom{12}{k}x^{2k-12}$ .
Set the exponent of $x$ to 4: $2 k - 12 = 4$ .
Solve: $2 k = 16 R i g h t a r r o w k = 8$ .
Compute $(8 12) = (4 12) = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = 495$ .
Thus the coefficient of $x^{4}$ is $495$ .

Common mistake: Misidentifying the correct

k

or computing wrong binomial coefficient

Concept tested: Coefficient of a term involving $x$ and $1/x$