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

Solution:

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

Binomial expansion of an exponential term states that:

(x + y)ⁿ = ⁿΣ_{r = 0} nC_r x^{n - r} × y^r where,

ⁿC_r = n!/ (n - r)!r!

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

(x + 2)⁵ = ⁵C₀x⁵ × 2⁰ + ⁵C₁x⁴ × 2¹ + ⁵C₂x³ × 2² + ⁵C₃x² × 2³ + ⁵C₄x¹ × 2⁴ + ⁵C₅x⁰ × 2⁵

The third term from this expansion is equal to  ⁵C₂x³ × 2².

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

Summary:

The third term from this expansion is equal to  ⁵C₂x³ × 2².