If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion of the (3z- 2y)" is 1.

Q: /Find the sixth term in the expansion (x- 2y)"

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Q: The first term in the Binomial expansion of (3x-y) is: None |(3x)y |(3x)6 |(3x)®y 1

A: general term of binomial exxpanson (a+b)n is Tr+1=nran-rbr

Q: Determine the first four terms in the binomial expansion of (-3-2x¹).

A: Here we have to open the binomial expansion.

Q: Find the specified nth term in the expansion of the binomial. (x - y)², n = 2

A: We need to find nth term.

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Consider the given expression. y3-12c29 The binomial formula is defined as,  a+bn=∑k=0nnkan-kbk As,…

Q: (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x?.

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Q: Find the specified nth term in the expansion of the binomial. (x + 2z)7, n = 4

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Q: What is the 5th term in the expansion of (x^3-1/x^2)^10?

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Q: Use binomial theorem to expand (2+X)5 in ascending powers of x up to the terms containing x3  and…

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Q: Find the coefficient a of the given term in the expansion of the binomial. (4x-y)to the power of…

A: Explanation of the solution is given below....

Q: Find the coefficient of x^2 in the expansion of (x+y)^12

A: This is a binomial expansion problem. Here we can use general concept of expanding a binomial…

Q: Find the term with no x in the expansion of x 15

A: we have to find the term with no x in the expansion of x3+12x-215.  as we know that the (r+1)th term…

Q: Give a combinatorial interpretation of the coefficientof x6 in the expansion (1 + x + x2 + x3 +⋯)3.…

A: According to the given information, it is required to give a combinatorial interpretation of the…

Q: Find the binomial expansion of f(x) = in ascending powers of x, up to and (243x)3 including the term…

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Q: Find the coefficient of x4 in the expansion of 1 +

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Q: Find the term indicated in the expansion .

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Q: 4. Find the coefficient of the term containing x' in the expansion of (x-2y)“.

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Q: Find the Term that free from x of the expansion (x2 +10

A: Given expansion(x2+(2/x3))10 a=x2 and b=2/x3, n=10 Formula  General term formula is, Tr+1= nCr…

Q: Give a combinatorial interpretation of the coefficientof x4 in the expansion (1 + x + x2 + x3 +⋯)3.…

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Q: Find the specified nth term in the expansion of the binomial. (x – 10z)7, n = 4

A: Known fact: The (r+1)th term in the binomial expansion of x+yn is given by Tr+1=nCr xn-r yr.

Q: Use the Binomial Theorem to find the coefficient of x° in the expansion of (3x-1) The coefficient of…

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Q: 4. Find the expansion of (x + y)6 using Binomial Theorem.

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Q: Write down the expansion of : 4 1 3x 2 by the binomial theorem.

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Q: Find the term containing x in the Expansion of (x +3 y)*

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Q: How many terms are there in the expansion of (4.x + 7y)0.+ (4x- 7y)10 ?

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Q: What is the coefficient of the term containing x^4 in the expansion (x - (2/x^2)^10?

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Q: Use Binomial Coefficients of x10y3 in the expansion of (x+2y)13.

A: Here the given expansion of (x+2y)13.  the general term of these series is

Q: What is the fifth term of the expansion of (x^2 + 1/x)^10?

A: What is the fifth term of the expansion of (x^2 + 1/x)^10?

Q: Give a formula for the coefficient of xk in the expansion of (10x + 20/x)100, where k is zero i.e.…

A: Given that 10x+20x100 The objective is to find the formula for the coefficient of xk. By binomial…

Q: What is the 5th term in the expansion of

A: The 5th term of the given expansion is solved by using binomial expansion formula (X+Y)^n.

Q: Which member of binomial expansion of (2x^3 + x^-1)^10 contains x^6 ?

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Q: Find the sixth term in the expansion (x-2y)"

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Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

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Q: Use the Binomial Theorem to find the coefficient of x' in the expansion of (x+3)" ...-.

A: on using binomial theorem we get the coefficient of x^7 that is

Q: Find an expression, in terms of n for the coefficient of x in the expansion (1+4x) + (1+4x)² +…

A: ANSWER :

Q: 4) Find the Term that free from x of the expansion (x2 +10

A: Use binomial expansion:-

Q: 11. Find the fifteenth term in the expansion of (x2 - -) 18

A: Given that, x2-1x18 We have to find the fifteenth term in the expansion of x2-1x18, By using, The…

Q: If in the expansion of (1 + n}+", the 5th term is 24 times the 3rd term, fnd the value of n.

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Q: Find the first 4 terms in the expansion of (2 + x²)° in ascending powers of x.

A: Given expression: 2+x26  ……1   To find: First 4 terms (in increasing power of x) in the expansion of…

Q: The coefficient of x²y* in the expansion of (4x-y)° is 240. True False

A: As we know the formula for expansion (a+b)n=C0nanb0+C1nan-1b1+C2nan-2b2+.......+Cnna0bn   Here, a=4x…

Q: Therefore, the 3rd term in the expansion of (x – 10z)’ is as follows. 7! 7C2x7 - 2(-10z)? 5! (-10z)?…

A: Therefore, the 3rd term in the expansion of  (x-10z)7 is as follows.   7C2x7-2(-10z)2=7!5!2…

Q: Find the expansion of (x + y)4 using Binomial Theorem.

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Q: Find the term independent of x in the expansion of 3 1 - 2r

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Q: Find the specified nth term in the expansion of the binomial. (x + 2z)7,    n = 6

A: Given:

Q: Use the binomial theorem to identify the coefficient of x° in the expansion: (2x + 1)4

A: Consider  (2x+1)4

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given To evaluate

Q: Use the Binomial Theorem to find the coefficient of x' in the expansion of (x + 3)1. ......

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Q: Find the coefficient of x2 in the expansion of (x – 1)37. -

A: Answer

Q: n what the coefficient of in the 13 expansion (x- 3y) of

A: