Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ 5 n 4 10 2 Thus, the value of n is 10. Question 9: Expand using Binomial Theorem Solution 9: x 2 1 2 x 4 x 2 1 , x 0 2 x 4 3 2 2 3 4 n x n x 2 n x 2 n x 2 n 2 C0 1 C1 1 C2 1 C3 1 C4 2 2 x 2 x 2 x x 4 3 2 x x 2 x 4 x 8 16 1 41 61 x 4 1 2 3 4 2 2 x 4 x 2 x x 4 3 x 8 x 24 24 32 16 16 1 1 6 2 3 2 4 2 x 2 x x x x x 4 3 x 8 x 8 24 32 16 1 1 6 .... 1 2 3 4 2 x 2 x x x x Again by using Binomial Theorem, we obtain 4 2 3 4 4 4 4 3 4 2 4 3 4 0 1 2 3 4 x x x x x 1 C 1 C 1 C 1 C 1 C 2 2 2 2 2 4 3 4 x x x x 1 4 6 4 2 4 8 16 2 3 4 3x x x 1 2 x ...... 2 2 2 16 4 3 3 3 3 3 2 3 3 C0 C1 C2 C3 x x x x 1 1 1 1 2 2 2 2 2 3 3x 3x x 1 ....... 3 2 4 8 From (1), (2) and (3), we obtain x 2 1 2 x 4 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ 1 2x 1 6 2 2 16 x 2 4 8 x x x x 2 3 4 2 3 3x x x 8 3x 3x x 8 24 32 16 2 3 4 3 4 3 2 x x 8 2 8 24 32 16 1 2x x 12 6x x 6 2 3 4 2 2 16 x x x x x 2 3 4 16 8 32 16 x x x 2 3 4 4 x 5 x x x x 2 2 16 Question 10: Find the expansion of 3 Solution 10: 3x 2ax 3a 2 2 Using Binomial Theorem, the given expression 2 2 3x 2ax 3a 3 using binomial theorem. 3x 2 2ax 3a 2 3 3 2 3 2 3 3 2 3 3 3 2 3 3 2 2 2 3 2 2 2 3 2 3 C0 x ax C1 x ax a C2 x ax a C3 a 3 3x 2ax 3 9x 12ax 4a x 3a 3 3x 2ax 9a 27a 2 4 3 2 2 2 2 4 6 3 3x 2ax 81a x 108a x 36a x 81a x 54a x 27a 2 2 4 3 3 4 2 4 2 5 6 3 3x 2ax 81a x 108a x **11**7a x 54a x 27a 2 2 4 3 3 4 2 5 6 Again by using Binomial Theorem, we obtain 3 2 3x 2 ax 3 3 2 3 2 2 3 2 3 3 2 2 3 2 2 3 3 C0 x C1 x ax C2 x ax C3 ax 27x 3 9x 2ax 3 3x 4a x 8a x 6 4 2 2 2 3 3 27x 54ax 36a x 8a x 6 5 2 4 3 3 From (1) and (2), we obtain 3 3x 2ax 3a 2 2 ……. (2) ………. (1) 27x 54ax 36a x 8a x 81a x 108a x **11**7a x 54a x 27a 6 5 2 4 3 3 2 4 3 3 4 2 5 6 27x 54ax **11**7a x **11**6a x **11**7a x 54a x 27a 6 5 2 4 3 3 4 2 5 6 can be expanded as Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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