The middle term in the expansion of 8 +2y is - (a) 35x*y (b) 70x*y (c) 140x'y (d) 35x*y 2.3

Q: 4) Find the 5th term of (x+ y)°

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

A: Here we have to open the binomial expansion.

Q: Find § 6-42 (Z+3) by Residue Theorm.

A: We have to evaluate the integral ∫ 6-4zz2z+3dz using the residue theorem. For this, we have to find…

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

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Q: Write the binomial expansion for (x +2y). (x+2y)® -

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Q: Use the the Binomial Theorem to calculate 11^11 (just giving the end result is not enough.)

A: To find the value of 1111 using the binomial theorem. Now, the Binomial expansion of (1+x)n is:…

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: In the expansion of (3x + 2y) °, the term 90, 72028 yl2 is the 4th term 5th term O 7th term O 6th…

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Q: Expand with help of Binomial Theorem (- +)

A: Using the Binomial theorem, the binomial expansion formula for (a+b)n is given by the formula,…

Q: Exercise 13 Determine how many times 0 appears in the multiplication table for Z16 -

A: Here, ℤ16=0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15It is a group under ⊕16 But we have to find the…

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

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Q: Explain/show how to find the fifth term in the expansion of the binomial (2r + 3y) by using the…

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Q: Find the coefficient of x²y in the expansion of (-4x + y)°. Give your answer as an integer.

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

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Q: Use binomial theorem to find the constant term (x-1/x)*8

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Q: Find the term indicated in the expansion (x3 + y2)8; sixth term.

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Q: Find the term indicated in the expansion (x + 2y)6; third term.

A: Find the term indicated in the expansion (x + 2y)6; third term.

Q: What is the 5th term in the expansion of (x^3-1/x^2)^20?

A: To find the 5th term in the expansion of x3-1x220.

Q: What is the middle term of the expansion (æ² – 4)* - 43750x^8 59080x^8 43500x^8 17920x^8

A: We will find middle term as

Q: Explain how to expand (a + b)' using the binomial theorem n an-kbk. Be specific. k expression, k-0

A: Given:      a+b7 The binomial theorem:        a+bN=∑n=0NNnaN-nbn where Nn=N!n!N-n!

Q: Find the term indicated in the expansion: (x2 + y3)8; sixth term.

A: To find the sixth term of expansion x2+y38

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

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Q: Use the binomial theorem to expand (1-x)^5

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Q: Expand and simplify using Binomial Theorem : ( 2a / 5 - 10b)^4

A: Given:  ( 2a / 5 - 10b)^4 Expand and simplify

Q: Explain what the pattern of exponents will be for the expansion of the binomial (6x – 7y)". Be…

A: Binomial Expansion Formula (p+q)n=∑nCii=0n×pn-i(q)i p=6xq=-7yn=10

Q: Explain recursion relation.

A: A recurrence relation is an equation that recursively defines a sequence where the next term is a…

Q: 10 What is the 6th term of (x − 1)¹⁰-

A: To find 6th term of x-110. Formula for general term of expansion of a+bn is given as -…

Q: Find the recursive and explicit rule for -1, 3, 7, 11,... Recursive rule

A: This is a problem of series . Based on concepts and formulas we will answer the question.

Q: 8. Use the binomial theorem to expand (3x - 4)4.

A: Expan using binomial theorem.

Q: How can the sum of k * (n choose k) = n(2 to the power of n-1) be proven akgebraically ?

A: Step 1: We have to prove that, Now by the binomial theorem, Now, differentiating the both sides 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: Which term of the expansion of (x + 7)° contains x° Term number contains x°.

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Q: Explain how to expand (a + b)7 using the binomial theorem expression, a"-kb. Be specific.

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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: Find the coefficient of the term involving x* in the expansion of 3x – - -262444 c. -252440 а. b.…

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Q: Use binomial theorum to expand (1 + 1/x)^7

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

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Q: Expand 10 (x − 4y) by binominal theorem.

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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: What is the coefficient of z^4 in the expansion of(z^3+3z+1)^5?

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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: What is the coefficient of the 3rd term from the beginning in the expansion of the expression ( 2x-…

A: Given: a2x-y6

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 expand the expression (3x + 2y?)°. Show your work.

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Q: What is the largest coefficient in the expansion of (x +1)8?

A: Answer is mentioned below

Q: d the image of the point (-2,4) under the expansion with factor 2 in the direction. ) (2,8) (-2,8)…

A: Given query is to find image of the point after expansion.

Q: Show all your steps. Find the coefficient of the term in the expansion of (3x – 4y)°.

A: The given expression is 3x-4y8. We have to find the co-efficient of x6y2. The binomial expansion is…

Q: Find the expansion of (2x-3)6 using Binomial Theorem.

A: Here we use combination to find the coefficients in the expansion of given polynomial and use…