Which is the correct expansion of (z +4y)³ using the binomial theorem? ° (z + 4y)² = (3) (z)³(43)° + (³) (²)}² (w)² + (2) (-)³(w)² + (3) (-2°(43)³ ○ (z+4y)² = (4) + (z)²(4y)³¹ + (z)¹ (4y)² + (z)³(49)³ * (z + 4y)² = (3) (43)³¹ (2)° + (³) (4³(z)³¹ + (2) 4)³(2³² + (3) 4°(z)³ O (z+4y)² = (z) (4y) + (z)³¹ (4y)² + (z)² (4y)² + (z)³ (4y)³

Q: x²+ 2x+3 10) Using the function f (x) %3D (1+x)(2+x)(1-x) a) Express in partial fractions b) Hence…

A:

Q: using binomial theorem up to the term in x

A:

Q: (x/3y+3y/x)^8 expand using binomial theorem

A:

Q: (2x2 + 3)3 1. (5x3 + 5)3

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the remaining…

Q: Evaluate z' if z = [1 + (x² − 1)³] ²³ O a. 2(2²-1)² (1+(2²_1)²³) i O b. none of these О с 41(2²-1)²…

A:

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

A:

Q: What is the characteristic polynomial for the recurrence relation an = 4an-1 + 8? (1) (x+4)(x - 1)…

A:

Q: Write the expansion of (1+ x)" as a linear combination of the polynomials rk. That is, determine the…

A:

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: E(3k? – 2k + 3(-1)k)

A: Given,  ∑k=110(3k2-2k+3(-1)k)

Q: Using the binomial expansion n (1 + x)² = ± (1) x², k=0 prove the following relations n n…

A:

Q: Expand with help of Binomial Theorem (- +)

A: Using the Binomial theorem, the binomial expansion formula for (a+b)n is given by the formula,…

Q: (7) Use congruences to prove the following. They were proven by induction in Prob- lem 19 in Section…

A: (a) To prove that 9 divides (4^n+15n-1), we need to show that (4^n+15n-1) is congruent to 0 mod 9.…

Q: Prove-that '(2) r' (₂+1) ¹ (2+ |) T(₂) nd thus derive Legendre's duplication formular 2' (2) T(2:)…

A:

Q: Prove the ..... Pr |P2n-1 Pn (− 4 ) = ² ( − 12 ) Pan ( 1 ) + ¹³ ( − 1) ³²2-1 (9) + + (-))) 2 P211

A:

Q: (b) (ii) Show that the binomial expansion of(1 + x) + (1-x) up to the term in x² is 2- 16 Hence, by…

A: The binomial expansion of the (1+x)k is given by (1+x)k = 1+kx+k(k-1)2!x2+k(k-1)(k-2)3!x3+........

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: Use the binomial theorem to expand the following: (a) (x + 2y)* (c) (3x + 1)4 (b) (x - y)6 (d) (x +…

A:

Q: -3)=-32

A: -8(x-3)=-32 -8x + 24 = -32 -8x = -32-24 -8x = -56

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: Use the binomial theorem to find the value of (3 + 21)4 where i is the imaginary unit. The Binomial…

A:

Q: f(x+h)-f(x) 5) Simplify the difference quotient for f(x) = x+ using the Binomial Theorem. h Show…

A: Quotient using binomial expansion

Q: 7) Use binomial theorem to expand (2x-1)^6

A:

Q: I am working on Discrete math, specifically Binomial Theorem and Pascal's Identity. I am trying to…

A:

Q: (3) VL1, L2 ((L1 L₂ L₁*)* = (L2 U L₁)*). O True

A: True.  this statement generally

Q: or binomials does p(x<2)=p(x<=2)

A: X~Binomial(n , p)  __________________________ P(X = x) = nxpx(1-p)n-x ; x = 0,1,2,..,n

Q: 11. Which is the correct expansion of (x + 4y) using the binomial theorem? O(x+4y)³ = (x) (4y) +…

A:

Q: Give a recursive definition of Binomial coefficient () in terms of (") (we assume n2 k). Do not…

A: The objective is to give the recursive definition of Binomial coefficient  n+1k+1 in terms of…

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: While proving n+2)2n+2) is an integer for the case n = 6q + 5 which of the following will be…

A: Given that  n(n+1)(2n+1)/6 Plug n=6q+5

Q: Determine the coefficient of the x'y term in the expansion of (2a + 3y) 2.

A:

Q: Find the Laurent expansions of the following around z = = 0: (i) (z – 3)-1, valid for |2| > 3; (ii)…

A: Answer

Q: The Taylor expansion of f for x→ 10 is f(x) = 10 + 3(x-10)² + 2(x-10)³ + 0((x a) ft (10) = -12 6) fr…

A:

Q: 2 + х2 — 1 х — 1 х+1 5х 1

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