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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 ( ) .
Worksheet 4.12 The Binomial Theorem Section 1 Binomial Coefficients and Pascal’s Triangle We wish to be able to expand an expression of the form (a + b)n. We can do this easily for n = 2, but what about a large n? It would be tedious to manually multiply (a+b) by itself 10 times, say.
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 .
a) Expand 4 6− x as an infinite convergent binomial series, up and including the term in x 3 . b) State the range of values of x for which the expansion is valid.
If we wanted to expand a binomial expression with a large power, e.g. (1+x)32, use of Pascal’s triangle would not be recommended because of the need to generate a large number of rows of the triangle. An alternative method is to use the binomial theorem. The theorem enables us to expand (a + b)n in increasing powers of b and decreasing powers ...
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.
Binomial Expansion Worksheet. Answers: Expand completely. 3) (2b- 5) (2y4 - 7) (3x2 - 9) (2y2 - Find each coefficient described.
