a) Obtain the expansion for (3 + 2x)* in ascending powers of x b) Find the term independent of x: 3 x2 - 5x3 ) 10 c) Obtain the expansion of ; 1-3x2 up to the term in x8 3.

Q: Expand (7 – 3x)“ in ascending powers of x, up to and including the 4" term. Hence, approximate…

A: We know (n+1)! = (n+1) n! Crn = n!(n-r)! r!

Q: 2x+ 3 2 X 6

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

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

A: We need to find the coefficient of x9 in the expansion of (x+1)14 + x3(x+2)15 .

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: Find the binomial expansion of f(x) = in ascending powers of x, up to and (243x)3 including the term…

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Q: Find the term indicated in the expansion .

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Q: Find the coefficient at x in the expansion of (3 + x)75

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Q: Find the  coefficient of x^5 in the expansion of  (1−2x)^8.

A: Given,             (1-2x)⁸ = (1+(-2x))⁸

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

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Q: Find the independent term of x in the expansion of [x|3 3 3 2x² + 10

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Q: Find the 3rd term in the expansion of (a + b)6 in simplest form.

A: Given (a+b)6 We need to expand and find the third termgeneral expansion of (a+b)n (a+b)n=∑k=0n nk…

Q: 6. When the terms are arranged in descending powers of x, determine the middle 10 term in the…

A: Given below the detailed solution

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

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Q: Find the 3rd term in the expansion of (x-3)^7

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Q: 14 Which term of the expansion of (x + 1)contains x 16 Term number contains x16

A: The given expression is:…

Q: Find the term in the expansion of (x2 + y2)5 containing x4 as a factor.

A: The given expression is x2+y25 To find the term containing x4 as the factor

Q: How many terms are there in the expansion of (4.x + 7y)0.+ (4x- 7y)10 ?

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Q: Find the term that contains x^8 in the expansion of (3x-1)^11

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

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Q: (a) Find the binomial expansion of (1+ x³)$/² up to and including the x term.

A: Given term is 1+x352

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: The Binomial Theorem is the method of expanding an expression which has been raised to any finite…

Q: When the terms are arranged in descending powers of z, determine the middle 8 3 term in the…

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

A: The given expression is,

Q: 11. Find the fifteenth term in the expansion of (x2 - -) 18

A: Given that, x2-1x18 We have to find the fifteenth term in the expansion of x2-1x18, By using, The…

Q: Obtain the expansion for (3 + 2x)* in ascending powers of x

A: According to binomial expansion,  a+bxn=an+n1an-1bx+n2an-2b2x2+n3an-3b3x3+....+nn-1abn-1xn-1+bnxn…

Q: Find the first 4 terms in the expansion of (2 + x²)° in ascending powers of x.

A: Given expression: 2+x26  ……1   To find: First 4 terms (in increasing power of x) in the expansion of…

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

A:

Q: find the fourth term in the expansion of  (x +  1   9…

A: Recall the fact that the general term of expansion ( a + b )n is as follows.

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: The binomial theorem states that for any real numbers a and b, (a +b)" = E o (") a"-* for any…

A:

Q: Infer a formula for Ak using factorization where A =

A: Calculate eigenvalues: 1-λ-62-6-λ=0-6+6λ-λ+λ2+12=0λ2+5λ+6=0λ=-2,-3

Q: Which term of the expansion of (x + 7)° contains x° Term number contains x°.

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Q: Consider the following expression. (x + y)8 Use the Binomial Theorem to find the expansion. (Enter a…

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

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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 fourth term in the expansion of ( 2x 10 ? -

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given To evaluate

Q: Find the 2nd term in the expansion of (a + b)° in simplest form.

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

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Q: Find the term of free x in the 10 2 expansion of (x² + 3)¹0.

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Q: Find the 7th _term in the expansion of : 5 2x 4x

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Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: To get the term that contains y9, use the binomial expansion and obtain the second term.…