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a) Find the first four terms in ascending powers of x in the binomial expansion of f x ( ) and in the binomial expansion of g x ( ) . b) Hence determine the coefficient of x 2 in the binomial expansion of h x ( ) .
If a and b are distinct integers, prove that a − b is a factor of an − bn, whenever n is a positive integer. [Hint: write an = (a − b + b)n and expand] Solution : a n = [ (a - b) + b] n. a n = n C 0 (a-b) n + n C 1 (a-b) n-1 b 1 + n C 2 (a-b) n-2 b 2 + n C n-1 (a-b)b n-1 + n C n b n.
10 Ιουν 2024 · The binomial theorem is a formula for expanding binomial expressions of the form (x + y) n, where ‘x’ and ‘y’ are real numbers and n is a positive integer. The simplest binomial expression x + y with two unlike terms, ‘x’ and ‘y’, has its exponent 0, which gives a value of 1
The binomial theorem states the principle for expanding the algebraic expression (x + y) n and expresses it as a sum of the terms involving individual exponents of variables x and y. Each term in a binomial expansion is associated with a numeric value which is called coefficient.
Binomial Theorem to expand polynomials explained with examples and several practice problems and downloadable pdf worksheet.
Find the value of the constant n in each of the following binomial expansions a) ( ) 1 3+ x n , if the coefficient of x 2 is 54 . b) ( ) 1+ x n , if the coefficient of x 2 is 55 .
The Binomial Theorem. Find each coefficient described. 1) Coefficient of x2 in expansion of ( 2 + x)5. 80. 3) Coefficient of x in expansion of ( x + 3)5. 405. 5) Coefficient of x3y2 in expansion of ( x − 3 y)5. 90.
