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 5C2x3 × 22.
Go through the explanation to understand better.
Binomial expansion of an exponential term states that:
(x + y)n = nΣr=0 nCr xn – r × yr where,
nCr = 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.