1. Find the coefficient of 2³6 in the expansion of 6 (1 +5x²5 + 12x50⁰) (x+x² + x³ + x¹ + x³ +rº + x² + x³ + x³ +: - x² + x¹0) ¹ "¹(E) Σ

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

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

Q: 1) (a) Determine the simplest form of the expansion of (2x4 - 1) 4. 4x (b) Determine the coefficient…

A: Consider,(1) (a) Given,(2x4−4x1​)4use the binomial theorem formula to simplify the given…

Q: When multiplied out, what are the first 4 terms of (x + 3y)0?

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Q: In Z2, 1 + 1 + 0 + 1 = 1 and 1 + 1 + 1 + 1 = 0.

A:

Q: 2. Expand by multiplying 'o) a) (3x+ 4)(2x - 2) b) (2x - 7)(-4x + 5) c) -4y(-4x -5y)

A: Given  a) (3x+4)(2x-2) Multiplying,  (3x+4)(2x-2) = (3x)(2x-2)+4(2x-2)…

Q: Find the product for the fraction 2/7×1/2

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Q: The coefficient of x²y4z5 in the expansion of (3x+y+z)¹¹ is

A: The given expression is: (3x + y + z)11 To find: The coefficient of x2y4z5 in the expansion of (3x +…

Q: pansion of (x + 3) ¹7+ x³(x+ 17 3

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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: 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: ) Write the expansion of (3 + 2x) and use the first three terms of the expansion to approximate3.26.

A: Concept is binomial theoram  3.2 = (3+0.2) 0.2 = 2x0.1

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

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Q: 32)Multiply: (x + 5)2(x + 3)

A: To multiply: (x+5)2(x+3)

Q: Answer the following: a) What is the general term of (x-y)xy? b) In the expansion of (1+x)^n the…

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

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Q: Compute the constant term in the expansion of (2x³ + ½)¹².

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Q: Compute the coefficent of x8    in the expansion of (3x -2)13

A: The given expression is,

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: 2 S²3 (x²-3x+18) 9x-X³

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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: (d) an 10"+1 +3 x 4"-1+5 is divisible by 9 for all n2 1,

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Q: Find the coefficient of x33 in the binomial expansion of (2x3 + 3x2)13

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Q: a) Determine the coefficient of x^3*y^4 in the expansion of (2x+y)^12. b) Determine the coefficient…

A: The objective of the question is to find the coefficients of specific terms in the expansion of…

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

A: By Binomial theorem (a+x)n=∑m=0nncman-mxm Here (x+1)14=∑m=01414cmx14-m1mNow the coefficient of…

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

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

A: Given: a2x-y6