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   =

= 5C0 (100)55C1 (100)4.2 + 5C2 (100)322 5C3 (100)2 (2)3 + 5C4 (100) (2)45C5 (2)5

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

= 10040008000 – 1000800032 = 9039207968

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