# What is the third term of the expansion of (x + 2) is raised to the fifth power?

The Binomial Theorem is the method of expanding an expression that has been raised to any finite exponential power.

## Answer: The third term from this expansion is equal to ^{5}C_{2}x^{3 }× 2^{2}.

Go through the explanation to understand better.

**Explanation:**

Binomial expansion of an exponential term states that:

(x + y)^{n} = ^{n}Σ_{r=0} nC_{r} x^{n – r }× y^{r} where,

^{n}C_{r }= n!/ (n - r)!r!

Using this binomial expansion formula for (x + 2)^{5}, we get the expansion as:

(x + 2)^{5} = ^{5}C_{0}x^{5 }× 2^{0 }+ ^{5}C_{1}x^{4 }× 2^{1} + ^{5}C_{2}x^{3 }× 2^{2 }+ ^{5}C_{3}x^{2 }× 2^{3} + ^{5}C_{4}x^{1 }× 2^{4} + ^{5}C_{5}x^{0} × 2^{5}

### The third term from this expansion is equal to ^{5}C_{2}x^{3 }× 2^{2}.