Binomial Theorem Questions with Solutions

The binomial theorem gives the expansion of (a + b)^n for a positive integer n as the sum of terms nCr a^(n-r) b^r. This topic covers the general term T(r+1) = nCr a^(n-r) b^r, finding a specific term or the coefficient of a power of x, the term independent of x, the middle term(s), and properties of binomial coefficients. Almost every question is solved using the general term. Write T(r+1), simplify the power of x, and set it equal to the power you need (or to zero for the term independent of x) to find r. Remember that the expansion has n + 1 terms, so there is one middle term when n is even and two when n is odd. The sum of all binomial coefficients is 2^n. Practise the binomial theorem questions below, each with a step-by-step solution.