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binomial expression. For example, x + a, 2 x – 3y, 3 1 1 4, 7 5 x x x y − − , etc., are all binomial expressions. 8.1.2 Binomial theorem If a and b are real numbers and n is a positive integer, then (a + b) n =C 0 na n+ nC 1 an – 1 b1 + C 2 a – 2 b2 + ..... + nC r an – r br +... + nC n bn, where nC r = n r n r− for 0 ≤ r ≤ n
However, for higher powers like (98)5, (101)6, etc., the calculations become difficult by using repeated multiplication. 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.
List of Binomial Theorem Formula Class 11. Binomial formula helps to expand the binomial expressions such as x + a, (x - (1/x))4, and so on. Students can refer to the list of binomial theorem formula class 11 provided below: Binomial Theorem: (a + b) n = n C 0 a n + n C 1 an - 1b + n C 2 a n – 2b 2 + ...+ n C n – 1 a.b n - 1 + n C n b n ...
Let us have a look at the following identities done earlier: (a+ b)0 = 1 a + b ≠ 0 (a+ b)1 = a + b (a+ b)2 = a2 + 2ab + b2 (a+ b)3 = a3 + 3a2b + 3ab2 + b3 (a+ b)4 = (a + b)3 (a + b) = a4 + 4a3b + 6a2b2 + 4ab3 + b4 In these expansions, we observe that. The total number of terms in the expansion is one more than the index.
Explain the concept of the Binomial Theorem covered in Chapter 8 of NCERT Solutions for Class 11 Maths. The Binomial Theorem is the process of algebraically expanding the power of sums of two or more binomials.
☛ Download Class 11 Maths Chapter 8 NCERT Book. Topics Covered: The topics under class 11 maths NCERT solutions chapter 8 are using the binomial theorem to expand expressions and finding the general term as well as the middle term in an exponential expression.
Solution: 102 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, binomial theorem can be applied. It can be written that, 102 100 2. 102 . 5. 100. 5 2 . 5 C . 5 100.
