from a handpicked tutor in LIVE 1-to-1 classes

# What is the coefficient of the last term in the binomial expansion of (x + 1)^{9}?

**Solution:**

Given, (x + 1)^{9}

We have to find the coefficient of the last term in the binomial expansion of (x + 1)^{9}

The binomial theorem or binomial expansion expresses the algebraic expansion of powers of a binomial.

The binomial expansion formula for (a + b)^{n} = ^{n}C_{0} (a^{n}b^{0}) + ^{n}C_{1} (a^{n-1}b^{1}) + ^{n}C_{2} (a^{n-2}b^{2}) + ^{n}C_{3} (a^{n-3}b^{3}) + ........... + ^{n}C_{n} (a^{0}b^{n})

Here, a = x, b = 1 and n = 9.

Substituting the values in the formula,

^{9}C_{0} (x^{9}{1}^{0}) + ^{9}C_{1} (x^{9}^{-1}{1}^{1}) + ^{9}C_{2} (x^{9}^{-2}{1}^{2}) + ^{9}C_{3} (x^{9}^{-3}{1}^{3}) + ........... + ^{9}C_{9} (x^{0}{1}^{9})

The last term is ^{9}C_{9} (x^{0}{1}^{9}

The coefficient of the last term = ^{9}C_{9} = 1

Therefore, the coefficient of the last term is 1.

## What is the coefficient of the last term in the binomial expansion of (x + 1)^{9}?

**Summary:**

The coefficient of the last term in the binomial expansion of (x + 1)^{9} is 1.

visual curriculum