Find an expression, in terms of n for the coefficient of x in the expansion (1+4x) + (1+4x)² + (1+4x)³ + ... + (1+ 4x)n.

Q: Find the first three terms of the expansion (4 – 2x)³.

A:

Q: Which of the following real number would be the coefficient of x in the binomial expansion of

A: Using binomial expansion formula find that there is no term of x in the binomial expansion of the…

Q: For the binomial expansion of (2x-3)^6, what is the coefficient of x^4?

A: Given data- We have given the expression (2x-3)6. We have to find the coefficient of x4. We know the…

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

A: Given: the coefficient of x2y4 in the expansion is 240

Q: Find the term indicated in the expansion (x2 + y)22; the term containing y14.

A: To find: The term containing y14. Given: The expansion is x2+y22. Concept used: If the expansion is…

Q: What is the coefficient of x9 in the expansion of (x+1)14 + x3(x+2)15 ?

A: We need to find the coefficient of x9 in the expansion of (x+1)14 + x3(x+2)15 .

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: a) Determine the fourth term in the following expansion (x + 3y)° 5r)5

A: The posted question has multiple questions. But according to guidelines we will solve the first…

Q: Find the coefficient of a-2 in the binomial expansion of  (27a2 - (1/81a3))9

A: Let us consider the expansion x+yn The binomial expansion is obtained as x+yn=∑k=0nCknxn-kyn

Q: Find the specified nth term in the expansion of the binomial. (x − 8y)5,    n = 3

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Q: – })* Q7. In the binomial expansion of (2 written in terms of descending powers of x, find: a. The…

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Q: 4. Find the 11th term in the expansion of 25 3r- + 5.x

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Q: The constant term in the expansion of the expression 4x is given by 15

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Q: What is the coefficient of x4 in the expansion of (x + 1)14 + x3 (x + 2)15?

A: The binomial expansion is given by,

Q: Find the coefficient at x in the expansion of (3 + x)75

A:

Q: Find the coefficient of x5in the expansion of (1 – 2x + 3x2)5

A: I have solved Algebraically

Q: Find the  coefficient of x^5 in the expansion of  (1−2x)^8.

A: Given,             (1-2x)⁸ = (1+(-2x))⁸

Q: Find the independent term of x in the expansion of [x|3 3 3 2x² + 10

A:

Q: Find the 3rd term in the expansion of (a + b)6 in simplest form.

A: Given (a+b)6 We need to expand and find the third termgeneral expansion of (a+b)n (a+b)n=∑k=0n nk…

Q: Find the coefficient of x4 in the expansion of (2-3x)6

A:

Q: Find the coefficient of x5 in the binomial expansion of (1 – 2x + 3x2)5

A: Solution:

Q: The term involving x^9 in the expansion of (x2 + 2/x)12 is

A: We are asked to fine the term that involving x^9

Q: 3. Find, in descending powers of x, the binomial expansion of (2 – r2)5

A: 3. In this question, we need to determine the descending powers of x in the binomial expansion of…

Q: Find the middle term in the expansion of (2/x + x/2)^14

A: The middle term in the binmial  expansion of (x+a)^n is (( n/2)+1)th term, if n is even . If nis…

Q: Q2: Find the first four terms in the expansion of (1 - x)-

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: In the expansion of 5x in descending powers of x, find the constant term in the expansion and state…

A:

Q: Find the coefficient of x¯² in the binomial expansion of 9 15 323 x²

A: According to the binomial theorem for an expression of the form x+yn, the binomial expansion would…

Q: In the expansion of ( 2x + 3 )°, find the sum of the coefficients of all the terms.

A: Consider the provided binomial expression. 2x+38 The expansion of the given binomial expansion is…

Q: Find the specified n-th term in the expansion of the binomial. (x- 8y)°, n = 3

A: The binomial expansion is a polynomial function  The binomial expansion of the expression (a+b)n is…

Q: Use the Binomial Theorem to write the expansion of the expression. (2√t-3)³

A:

Q: Write the first, third and fifth terms of the expansion of (3x – 5y)5.

A: Write the first ,third and fifth term of the expansion of (3x-5y)5.

Q: Find the specified nth term in the expansion of the binomial. (x - 8y)5, n = 3

A: Given (x - 8y)⁵, n= 3 We have to find the specified nth term in the expansion of the binomial.

Q: Find the indicated term in the expansion of the given binomial. The eighth term in the expansion of…

A: Given: y=x2-1x45 we know that r+1th term of a+bn is given by Tr+1=ncran-r.br…

Q: obtain the binomial expansion of (1-2x)^5 and use it to evaluate(0.98)^5 correct to 5d.p

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Q: Find, in descending powers of x, the binomial expansion of (2 - a2)5

A:

Q: Find the 2nd term in the expansion of (a + b)º in simplest form.

A: Solved below

Q: Find the 3rd term in the expansion of (x- 1)^5 in simplest form.

A: Given that we need to find the third term in the expansion of ( x - 1)5.

Q: What is the coefficient of r* in the binomial expansion of 1 (1 – 32?) Give your answer as an…

A: Given function is 1/(1-3x2).

Q: -1)º-k(x)' 18-6k 2512 k=0

A: to calculate the terms first we need to understand the calculation of 0! = 1 1! = 1

Q: What is the coefficient of x12y13 in the expansion of (2x+3y)25?

A:

Q: Find the indicated coefficient or term. The coefficient of x in the expansion of (3x+2)^5

A: Binomial theorem expansion of is

Q: What is the coefficient of x° in the expansion of (x + 1)14 + x³(x + 2)15?

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: What is the constant in the 6th term of the expansion of ((1/2)x – 3)^16?

A:

Q: What is the coefficient of x° in the expansion of (x + 1)14 + x² (x – 1)13?

A:

Q: Determine the coefficient of the 5th term in the expansion of (n – 2m)'.

A: n-2m7Apply binomial theorem:  a+bn=∑i=0nnian-ibia=n,…

Q: Find the 2nd term in the expansion of (a + b)6 in simplest form.

A: We can find the 2nd term as below