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} = _{n}C_{0} a^{n} + _{n}C_{1} a^{n1}b^{1} + _{n}C_{2} a^{n2}b^{2} +..........+ _{n}C_{n1} ab^{n1} + _{n}C_{n}b^{n},
where n = 0
Binomial Theorem also finds the coefficient of a term in the expansion.
Examples of Binomial Theorem

(x + 4)^{4} = x^{4} + 16x^{3} + 96x^{2} + 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 q^{3} in the expansion of (q  1)^{3}.
Choices:
A. 1B. 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} = q^{3}  3q^{2} + 3q  1
Step 2: The coefficient of q^{3} in the above expansion is 1.
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