8. The Laurent's expansion of (2² – 1) (2² + 4 for |z|<1 is 5z2 2125 1). 4 64 16 2) + 21 4 4 4 3) - 522 25 4 16 64 322 21z5 4) 을 16 32

Q: 6. What should be added from 2x +3x` -- x² -1, so that it becomes exactly divisible by (x-2)?

A:

Q: 9) x² + y² + 12x + 22y + 108 = 0 CX+67² + y +117²=49 CX-47² \ Cy-151²=9 CX-107² + (y +1272²=9 CX-5)…

A:

Q: (Proof by cases: (p₁ V P2 V (Pn →q)) Prove or disprove. V Pn) → q = (P₁ → q)^(p2 →q)^^...^ "The 4th…

A: Let x be any integer.  We need to prov        x4 does not leave remainder 2 when divided by 3.…

Q: each expression. – 76² + 76) + (5b² – 36* – 36) 4) (6v + 3v² – 6v) – (7»

A:

Q: 7a+48a + 36 \252 3.) Sp-41-36 a-5 :6 c:56 5n-49n+72 6.) 6x-x-12 -49 6 b=X5 0 4a-16a-15 4 -16 15 9)…

A: Given:      5v2-41v-36  Break the expression into group.      =5v2+4v-45v-36      =5v2+4v+-45v-36…

Q: I(f) = μετα fi + 3 +3 N-1 Σ fitfiti + + 2 i=2,5,8,... N-2 Σ i=4,7,10,... f; ] + fN+1

A: Given: Objective: To write the above formula in MATLAB.

Q: Use the binomial theorem to expand the binomial.

A:

Q: Prove that for all integers n.4n² +6n + 1 is not divisible by 4. Be sure to explicitly show how each…

A:

Q: If C₁ * x² = c(1) ²¹ + a₂ (1) ²³ t² is the complementary solution of the nonhomogeneous system 3…

A: If the nonhomogeneous system is x'=3-22-2x+-2tt4-1 If the complimentary solution is…

Q: Maximise Z = 5x1 + 6x2 Subject to X1 + x2 0 and integer

A:

Q: While proving "(n+1)(2n+1) , following will be obtained is an integer for the case n = 6q + 5 which…

A: We have to prove that : n(n+1)(2n+1)6 is an integer for n=6q+5 Substituting n=6q+5 in n(n+1)(2n+1)6…

Q: 23) Expand: 2x{x² + 1) - (x° + 5x - x* - 7) A) x* - x² - 3x - 7 B) x* + 2x - 3x -7 C) x' +x - 3x + 7…

A:

Q: 8(5-2)

A: We have to solve for z 8(5-z)/7=-z Now solve the equalities 8(5-z)/7=-z 8(5-z)=-7z 40-8z=-7z…

Q: 36 6 10. Find the coefficient of x³6 in (x + x² + x³ + x² + x³ + x² + x² + x³) ³

A: To find the coefficient of the term x36 in the expansion of x+x2+x3+x4+x5+x6+x7+x85.

Q: x(x²+1 V2x³ –1

A: to calculate thefollowing expressionlnxx2+122x3-1

Q: 25. Which is the correct expansion of (x + 4y)³ using the binomial theorem? O ○ (x + 4y)³ = (3)…

A: Given, (x+4y)3

Q: U10(20) = {1,11, 20}

A: U(n) is the group of units mod n and the operation on it is multiplication mod n. So U(n) will…

Q: For 1 De

A:

Q: 6. (6x – 15)' (2r+ 1)

A: To find x ?

Q: 36. Use the binomial theorem to expand (2x - y)* . A. 16x* – 32x³y + 24x²y² – 8xy³ + y* С. 2x - 4х3у…

A:

Q: Use the Binomial Theorem to expand the binomial (3x – 5y)*. 81x* + 625y* b. 81x* – 540x'y + 1350x²y²…

A: The expansion of 3x-5y4 by the help of Binomial Theorem is

Q: What is the degree of the largest irreducible factor of (x^12)-1 over ℚ?   3 4 6 None of the above

A:

Q: Ifx+y+z= 1 and x, y, z are positive, then show that ( 1)² ( 1)² ( 1)² 100

A:

Q: What is the Coefficient o x' y b. 24 in (3x +y)? Plow monomials appear in +he meny expansion of (3x+…

A:

Q: 10. By Binomial Theorem (2a – b)* =16a* – 32a’b+24a*b? – 8ab³ +b* | a. TRUE. b. FALSE.

A: We know the binomial therom expansion

Q: For what value of k is x+1 a factor of x^4+2x^3-3x^2+kx+1 in ℤ_5[x]?   1 2 3 4 None of the above

A:

Q: a) 9x-49 (4x+1)(3x-7) Restrictions for # 2 (a) 1 Restrictions for # 2 (b) x²+7x+6 (x+2)? x'+4x+4…

A:

Q: (-5) + 4 – 1+ 4- (-21) * (-7)) ova

A: Simplification

Q: State De-Moivre's theorem. Compute n" derivative of the function y th x² +a?

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: true or false  1.) If a │b then a │b^n for n ϵ N 2.) n^4 + 4 is composite for all n > 1 3.)If p is…

A: Due to our terms and condition I have solve just first three questions in your question. Please…

Q: 02 4 -6 -6 A 6 5 5 = B = 0 52 5 3 4 -2 4-2, 10 -3, Find the following expression: 1. 2A + 4B 2.0A +…

A: Given are the following matrices:The objective is to find the following:To multiple a matrix with a…

Q: expand about z=1 (z+1)(z-2)*

A:

Q: 10 Find the coefficient of x in the expansion of · (3x-1) "⁰.

A: Explanation of the answer is as follows

Q: H) (3x² + 4x – x' – 2x' – 4) + (x+ 2) 0) (2x³ – 2x² + 4x² – 3) + (x + 1) P) (-x* + 2x – 2x - 3x + 1)…

A: we have to divide