(c) How many strings of four decimal digits have exactly three digits that are 9? (d) Write down the coefficient of the x yt term in the expansion of (x + 2y)10.

Q: Solve this attachment.

A: We have to show ∑k=0n-1knk=0 using binomial theorem. We know by binomial  theorem…

Q: Given (x − y)108. Use the Binomial Theorem to find the coefficient of x106y2, the third term of the…

A: We have to find

Q: What are the first and last terms in the expansion of (5x + 4y)*?

A:

Q: 1. In your own words, what is the binomial theorem. Find the 5th term of (x+7)

A: Given : x+77

Q: What is the degree of each term in the expansion of (x+5y)^21 ?

A: The dree of the term is the sum of the powers of the variable.  Note that the binomial expansion of…

Q: 6. Find the coefficient of x in the binomial expansion of 3. , if exists. 2.x?

A:

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: What is the coefficient of aº in the expansion of (x + 2)15 + x*(x +3)20?

A:

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: Which is the correct expansion of (x+4y)^3 using the binomial theorem?

A:

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

A:

Q: Q4: Find the term independent of x in the expansion (1+

A: Binomial expansion is used.

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

A:

Q: 3. The fifth term in the expansion of (2x + k) is equal to the fourth term in the expansion of (2 +…

A:

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

A:

Q: Find the 7th and 11th term of the expansion (y − x)^14

A:

Q: Q3. (a) Find the binomial expansion of (1 + 4x)2 up to and including the term in x².

A:

Q: Use the Binomial Theorem to find the coefficient of x° in the expansion of (x- 1)º. .5

A: The term of x^5 is:

Q: (xt - 4y)" 12

A: Let's find middle term of given function.

Q: 24 + * ? 8 What is the coefficient for the yl8 term in the expansion of (5x°y²

A: We use the Binomial Theorem to answer the given question.

Q: 1. Find the coefficient of x5y3 in expansion of the expression (x + 3y)8 2. Sixteen people attend a…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 2. What is the value of the 3rd term of the expansion (3y- 2)'? | O - 10206y O 35a+b3 20412y5 O 21a…

A:

Q: 3 O Find the first three terms of the expansion of (1+x)(2x-1)

A: The given series is 3(x+1)(2x-1) We have to find first three terms of the given series. This can be…

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

A: ANSWER :

Q: 2 16 Use the binomial formula to find the coefficient of the y z term in the expansion of (2y-z)"°.

A:

Q: 14) Calculate the 5th term in the expansion of (x – 2y)7.

A:

Q: Find the sixth term in the expansion: (3x – 2y)".

A: Consider the given binomial expansion.

Q: 3. Find the expansion of (x + y)$ using Binomial Theorem.

A: The solution is given as

Q: Find the sequence {ax}k2o for the generating function G(x) = (x + 2)².

A:

Q: -1/2 p. Find the coefficient of x" in the expansion of (1– 4x)2.

A:

Q: Find the fifth term in the expansion of (x2 + y2)10

A:

Q: Use the Binomial Theorem to find the coefficient of x' in the expansion of (3x + 1)12 The…

A: The equation is 3x+112

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: Use the Binomial Theorem to find the coefficient of x' in the expansion of (2x - 1)°.

A:

Q: Find the 6" term in the expansion of (x + 3y )"

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 10 Find the coefficient of x in the expansion of · (3x-1) "⁰.

A: Explanation of the answer is as follows

Q: Find the 2nd term in the expansion of (3x + y) in simplest form.

A:

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 least coefficient in the expansion of (x -1)7?

A: Use Pascal's Triangles to find least coefficient in the expansion of (x -1)7

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

A: Consider  (2x+1)4

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

A:

Q: (i) Expand (x +y)³ by using Binomial Theorem (ii) Expand /1+y _up to three terms by using Binomial…

A: Given that: x+y3

Q: Suppose you are expanding (5x - 2y) a)i) How many terms are there in the expansion? )State the…

A:

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

A:

Q: Find the seventh term of the 10 expansion ( x+ y)º

A: We know that (x+y)n = ∑r=0nCrn xn-r yr Hence (x+y)10 = ∑r=010Cr10 x10-r yr

Q: 22 2 Use the binomial formula to find the coefficient of the z"x´ term in the expansion of (z- 3x)*.

A:

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

A: Answer