# Without expanding, find the value of (x + 1)4 − 4(x + 1)3 (x − 1) + 6 (x + 1)2 (x − 1)2 − 4(x + 1) (x − 1)3 + (x − 1)4 - Mathematics and Statistics

Sum

Without expanding, find the value of (x + 1)4 − 4(x + 1)3 (x − 1) + 6 (x + 1)2 (x − 1)2 − 4(x + 1) (x − 1)3 + (x − 1)4

#### Solution

Let x + 1 = a and x − 1 = b

We notice that 1, 4, 6, 4, 1 are the values of 4C0, 4C1, 4C2, 4C3, 4C4 respectively and

∴ the given expression becomes

4C0a4b04C1a3b + 4C2a2b24C3ab3 + 4C4a0b4

= (a − b)4

= [x + 1 − (x − 1)]4

= (x + 1 − x + 1)4

= 24

= 16

Concept: Binomial Theorem for Positive Integral Index
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.2 | Q 7. (i) | Page 77