Class 11 Maths Binomial Theorem | Binomial Theorem |

**Binomial Theorem**

We know how to find the squares and cubes of binomials like a + b and a – b. E.g. (a+b)^{2} , (a-b)^{3} etc. However, for higher powers calculation becomes difficult. This difficulty was overcome by a theorem known as binomial theorem. It gives an easier way to expand (a + b)^{n}, where n is an integer or a rational number.

Points to note in Binomial Theorem

- Total number of terms in expansion = index count +1. g. expansion of (a + b)
^{2}, has 3 terms. - Powers of the first quantity ‘a’ go on decreasing by 1 whereas the powers of the second quantity ‘b’ increase by 1, in the successive terms.
- In each term of the expansion, the sum of the indices of a and b is the same and is equal to the index of a + b.

Refer ExamFear video lessons for Proofs.

**Numerical**: Compute (98)^{5}

Solution: (98)5 = (100-2)5 =

= ^{5}C_{0} (100)^{5} – ^{5}C_{1} (100)^{4}.2 + ^{5}C_{2} (100)^{3}2^{2 }– ^{5}C_{3} (100)^{2} (2)^{3} + ^{5}C_{4} (100) (2)^{4} – ^{5}C_{5} (2)^{5}

= 10000000000 – 5 × 100000000 × 2 + 10 × 1000000 × 4 – 10 ×10000 × 8 + 5 × 100 × 16 – 32

= 10040008000 – 1000800032 = 9039207968

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