Use the Binomial theorem to find the value of $(3 + 4)^{4}$ .

easy 1 mark Class 11 · Mathematics · Binomial Theorem

Answer

2401

The correct answer is 2401 — Add all the terms: $81 + 432 + 864 + 768 + 256 = 2401$ .

Step-by-step solution

Write the expansion using the Binomial theorem: $(3 + 4)^{4} = \sum_{k = 0}^{4} (k 4) 3^{, 4 - k} 4^{, k}$ .
Compute each term: $k = 0 :, 1 c d o t 3^{4} = 81$ ; $k = 1 :, 4 c d o t 3^{3} c d o t 4 = 432$ ; $k = 2 :, 6 c d o t 3^{2} c d o t 4^{2} = 864$ ; $k = 3 :, 4 c d o t 3 c d o t 4^{3} = 768$ ; $k = 4 :, 1 c d o t 4^{4} = 256$ .
Add all the terms: $81 + 432 + 864 + 768 + 256 = 2401$ .

Common mistake: Using incorrect binomial coefficients or forgetting to multiply by the powers of 3 and 4

Concept tested: Binomial expansion of integer power