What is the coefficient of the term 3021 in the expansion of (2x - y)51 C(51,30) 230 C(51, 30) 220 C(51, 21) 230 -C(51, 21) - 230

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: 10 3 Consider the expansion of

A: Given that The aim is to find the coefficient of in So, to find r for the general term,

Q: In the expansion of (x+y)35

A: We use the Binomial Theorem to find the required coefficient in the given question.

Q: The expansion of (1 - x)® = A 1+4x - 7x² + . B 1- 4x + 7x2 - C 1+ 4x - 7x2 + Đ 1- 4x + 7x² – 23.

A: Please see the explanation below

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

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Q: In the expansion of + 6)-", state the number of terms and the coefficient or the middle term. 21, 20…

A: Introduction: The binomial expansion is a very important finite series in mathematics. With the aid…

Q: What is the coefficient of the following term

A: The binomial expansion of a series is given by the expression (x+y)n=∑k=0nCknxn-kyk. Thus, the…

Q: Which of the followings is/are in the expansion of (a+b)^6?

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Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: O write the expansion of : (3a+ 2b)$ , (4z – w) , - -→*

A: We have to expand the following expression by using binomial expansion

Q: What is the result of the following operation: (1,10) n (10) (A) 0 B) (1,10) (1,10) (1,10)

A: We have to find the intersection The intersection of two sets is the set of elements that are common…

Q: Add the polynomials (10z - 82 7æ³ - 10) + (- 4x + 12a + 7a + 9) | Submit Question

A: Add the polynomials. Solution is given below-

Q: If x is positive, the first negative term in the expansion of (1 + x)27/5 is (a) 5th term (b) 6th…

A: Introduction :

Q: for

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Q: In the expansion of (x + y)16 which term has the same coefficient as x14y2? O a. x12,4 Oc x3y14 O d.…

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Q: Determine the coefficients ao, a1, a2, a3 in the following expansion in terms of Legendre…

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Q: n (x - 1)" The sixth term of the expansion of x is 1287 8 X 3125 . Determine n.

A: Let us consider the expression a+bn. The binomial expansion of the given expression is , a+bn=C0n…

Q: In the expansion of (4x + y) ^ 9, the coefficient of x3y4 is

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Q: What is the term involving a6 in (a² + ¹)1¹²? a

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Q: Find the coefficient of x24 in (x + x2 + x3 + x4 + x5 )8

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Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

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Q: Multiply A321 -1 10 -7 0 Show your your work!

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Q: Еxercise 13 Determine how тany times 0 арpears in thе тultiplicatioп table for Z16-

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Q: What is the coefficient of 8 in the expansion of (x + 1)¹³ + x²(x + 2) ¹6 ? 13

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Q: a'b in (a + b)'07

A: a+b10 Now the general term is, Tr+1=Crn·an-r·br⇒Tr+1=Cr10·a10-r·br

Q: What is the coefficient of x^8 in the expansion of (2+x)^11?

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Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

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Q: What is the coefficient of (x^8)(y^12) in the expansion of (y+x)^20

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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: What is the coefficient of p5q5 in the expansion of (p+q)10?

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Q: I simplified 6. 3 - x + 5 7 1 + x - 4 3 – 6(x – 4) by multiplying by 1 and obtained - 1 + 7(x + 5)

A: We have, 3-6x+51+7x-4

Q: What is the coefficient of x4y2z6 in the expansion of (3x² + 2y + 3z3)6?

A: Apply binomial theorem and isolate the coefficient

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: Is it true that GCD(6,14,119) x LCM(6,143,119)= 6x143x119?

A: We know that GCD(a,b,c) × LCM(a,b,c) = axbxc

Q: What are the 5a + 20a - 60 factors of O 5 (x-6)(x+2) • 5 (x+6)(x-2) O 5 (x-6)(x-2)

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Q: What is the ab c³ term of the expansion of (a – b2 + 3c)??

A: According to binomial expansion, the (r+1)th term of the binomial (a+b)n is given by,

Q: Find the coefficient of x® in (1+ x² + x4 + x®)4.

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