# Ex 8.1,4

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 8.1, 4 Expand the expression 𝑥3+1𝑥5 We know that (a + b)n = nC0 an b0 + nC1 an – 1 b1 + nC2 an – 2 b2 + …. …. + nCn – 1 a1 bn – 1 + nCn a0 bn Hence (a + b)5 = = 5!0! 5 − 0! a5 × 1 + 5!1! 5 − 1! a4 b1 + 5!2! 5 − 2! a3 b2 + 5!3! 5 − 3! a2b3 + 5!4! 5 − 4! a b4 + 5!5! 5 −5! b5 × 1 = 5!0! × 5! a5 + 5!1! × 4! a4 b + 5!2! 3! a3 b2 + 5!3! 2! a2b3 + 5!4! 1! a b4 + 5!5! 0! b5 = 5!5! a5 + 5 × 4!4! a4 b + 5 × 4 × 3!2! 3! a3 b2 + 5 × 4 × 3!2 × 1 ×3! a3b2 + 5 × 4 × 3!3! ×1 ×3! a2b3 + 5 × 4!4! ab4 + 5!5! b5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5 Thus, (a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5 We need to find 𝑥3+1𝑥5 Putting a = 𝑥3 & b = 1𝑥 𝑥3+1𝑥5 = x35+ 5 x34 1x + 10 x33 1x2 + 10 x32 1x3 + 5 x3 1x4 + 1x5 = 𝑥5243 + 5 𝑥4811𝑥 + 10𝑥327 1𝑥 + 10 𝑥291𝑥3 + 5 𝑥3 + 5 𝑥3 1𝑥4 +1𝑥5 = 𝑥5243 + 581 𝑥3 + 1027 𝑥 + 109 1𝑥 + 53𝑥3 + 1𝑥5

Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.