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 = ⁿC₀ (aⁿb⁰) + ⁿC₁ (a^n-1b¹) + ⁿC₂ (a^n-2b²) + ⁿC₃ (a^n-3b³) + ........... +  ⁿC_n (a⁰bⁿ)

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

Substituting the values in the formula,

⁹C₀ (x⁹{1}⁰) + ⁹C₁ (x^9-1{1}¹) + ⁹C₂ (x^9-2{1}²) + ⁹C₃ (x^9-3{1}³) + ........... +  ⁹C₉ (x⁰{1}⁹)

The last term is ⁹C₉ (x⁰{1}⁹

The coefficient of the last term = ⁹C₉ = 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.