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This lesson covers skills from the following lessons of the NCERT Math Textbook: (i) 6.1- Introduction, and (ii) 6.2 - Binomial theorem for positive integral indices
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.
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.
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
The NCERT Solutions Class 11 Maths Chapter 8 covers two major topics namely - expansion of expressions using binomial theorem and pinpointing a term within an exponential expression. Both topics are very important and come with vital formulas.
Solution: 101 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, 101 100 1. 101 . 4. 100 1 . 4. 4 C . 4 3 2 2 100 4 C 100 1 .
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.
