In the expansion of a binomial (a + b)" the third term is equal to 56, the fourth term is 70, and the binomial coefficients of the third and the sixth term are equal. Find the values of a, b, and n.

Q: In the expansion of (2 + 4y?) a. How many terms are in the expansion after like terms have been…

A: We will find the answers of all parts using binomial expansion.

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: 4. Determine the binomial coefficients in the 4th row of Pascal's triangle and use them to expand 3x…

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 4th term of the expansion of (1 - 2x)" if the binomial coefficients are taken from the…

A: (1-2x)n binomial coefficients1 6 15 20 15 6 1

Q: Find the coefficient a of the term in the expansion of the binomial. Binomial Term (6x-y)^12 ax^4y^8

A: The given binomial 6x-y12

Q: Find the coefficient a of the term in the expansion of the binomial. Binomial Term (3x-y)^10 ax^2y^8

A: Binomial expansion:(a+b)n =nk ak bn-kfor: (3x-y)10: a=3x, b=-ya x2y8:Third term:k=2:(102) (3x)2…

Q: Determine the coefficient of a6b2 in the expansion of (a + b)8 by using the Binomial Theorem. That…

A: To find the coefficient of a6b2 using binomial expansion

Q: Find the coefficient a of the term in the expansion of the binomial. Binomial (z³ - t)13 3 = Term…

A:

Q: Using the expansion for the binomial: (x° + y°)° : 5.,12 We wish to find the coefficient for the…

A: The formula for binomial expansion is x+yn=∑r=0nCrnxn−ryr. The combination formula isnCr=n!n−r!r!.

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

A: Write the binomial expansion of the given polynomial than specified the nth term.

Q: use tge binomial formula to find the coefficient of the q24z term in the expansion of (q-3z)25

A:

Q: State and prove Binomial theorem and also find 18th term in the expansion of (2x - 3y)".

A:

Q: Find the coefficient a of the term in the expansion of the binomial. Binomial      Term (x2 + y)10…

A:

Q: Find the coefficient of x8y6 in the expansion of (2x2-5y3)6 by using the Binomial theorem.

A:

Q: What is the coefficient of the second term in a binomial that is raised to the sixth power? 5 15 20…

A:

Q: In a sample of 3840 families with 7 children, how many families would be expected to have 5 or more…

A:

Q: Find the middle term of the binomial expansion (5u3+4v2)10

A: There are 11 terms in the expansion of the binomial expression. The middle term is the 6th term.…

Q: he second, third and fourth terms in the binomial expansion (x + a)" are 240, 720 and 1080,…

A:

Q: Find the specified nth term in the expansion of the binomial. (x + y)11,    n = 4

A: For an expression of the form x+yr, the binomial expansion is given by- Tk+1=Ckrxr-kyk where n=k+1

Q: Expand the binomial by using Pascal's Triangle to determine the coefficients. (x - 2y)5

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: Find the coefficient a of the given term in the expansion of the binomial.

A:

Q: Use the binomial theorem to expand the expression (u - 5v)¹

A:

Q: 10. If the volurne of a box Is represented by the expression (x-3x2-10x+ 24) cm³ and its width Is…

A: We have to solve given problems :

Q: a) Write down the first term in the expansion of (x - 4)5 [Hint: Care is needed with the negative 4]…

A:

Q: What is the expansion of the binomial expression (x + y)⁵ ? What are the binomial coefficients?

A: Solution of given question is written in below steps.

Q: Find the coefficient of the indicated term in the expansion of the binomial.   x7 term of (x − 4)9

A:

Q: In the expansion of a binomial (a + b)" the third term is equal to 56 the fourth term is 70 and the…

A:

Q: Kerys is trying to expand the binomial (2x +y)* using the binomial theorem expression, a"-*b* What…

A: Given:      Binomial 2x+y4 The binomial expansion theorem states that            a+bn=∑k=0nnCkan-kbk…

Q: Find the binomial expansion of (3a+2b)^6

A: In this question, we find the binomial expansion of (3a+2b)^6.

Q: Find the 10th term of the expanded binomial (2x – 3y)11

A:

Q: How many five-digit numbers are there where an even number of the digits in the number are even?

A: The number of five digit numbers where aneven number of digits in the number are even=??For these…

Q: 1. Suppose when using the Binomial Theorem an expansion turned out to be the expression as shown…

A: Formula for Binomial theorem: a+bn=an+nan-1b+nn-12!an-2b2+nn-1n-23!an-3b3+.....+bn Given expression:…

Q: Find the coefficient of the indicated term in the expansion of the binomial.   a3b3 term of (2a +…

A:

Q: Find the coefficient of the indicated term in the expansion of the binomial. y3 term of (y + 9)4

A:

Q: . Explain how to use Pascal's Triangle to expand the binomial (3x-4y)".

A:

Q: Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11

A: Given data: The given expression is (3x-4y)11. Here, the power of the binomial expression is 11.…

Q: Determine if the term x^4 exists in the development of the binomial. 60 1 2x + 4x3 If it does not…

A:

Q: The degree of each term in the binomial expansion of (x – y)5 is 6 5 -5 4

A: The degree of each term in the binomial expansion of (x – y)5 is 6 5 -5 4

Q: We can use the binomial theorem to expand (3x+5)14 and (3+5x)14 as sums of terms (monomials).…

A: The two expression given are 3x+514 and 3+5x14Using binomial theorem and find out the common terms

Q: Which expression represents the difference of (8x³ +6x² + 5) and (5x³ - x²-3x + 1)? 3x³ + 5x² + 3x…

A:

Q: Consider the binomial theorem to expand (3x + 2y)^5. What is the coefficient of the x3y2 term? Thus…

A: we will use expansion of given expression for better understanding.

Q: Find the coefficient a of the term in the expansion of the binamial. Binomial (3x-ay): Term 2 8 ax

A: The general term of (x+y)n is given by:Ar+1=Crnxn-ryr  , r=0,1,2,....Then general term of (3x-2y)8…

Q: 28. The expansion of the binomial (x +y)2a +5 has 18 terms. The value of a is

A:

Q: (d) Evaluate 1.8* = (2 - 0.2)* directly and also as a sum of 5 terms using the Binomial Theorem.

A: the value of 1.84 directly is given by  1.84=1.8×1.8×1.8×1.8=10.4976 using the binomial theorem the…

Q: Find the fourth term of the binomial expansion (4a-b)6

A: