BINOMIAL THEOREM

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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.

    Choices:
    A. 1
    B. 0
    C. 3
    D. -1
    Correct Answer: A

Solution:

    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.

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