Definition of Binomial Theorem
Binomial Theorem is used to expand powers of binomials.
It States that :
(a + b)n = nC0 an + nC1 an-1b1 + nC2 an-2b2 +..........+ nCn-1 abn-1 + nCnbn,
where n = 0
Binomial Theorem also finds the coefficient of a term in the expansion.
Examples of Binomial Theorem
(x + 4)4 = x4 + 16x3 + 96x2 + 256x + 256
- The power of the binomial x + 4 is distributed using the binomial theorem.
Video Examples: Binomial Theorem
Solved Example on Binomial Theorem
Ques: Find the coefficient of q3 in the expansion of (q - 1)3.
Correct Answer: A
Step 1: Expanding (q - 1)3 by using the binomial theorem, we get (q - 1)3 = q3 - 3q2 + 3q - 1
Step 2: The coefficient of q3 in the above expansion is 1.