binomial theorem to expand (a2 _ 3)4 . Show your work.

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Q: -4 (3x² + 5x) 52

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Q: (15 points) Prove the ring Z[√−2] = {a+b√−2 | a,b ≤ Z} is a Euclidean domain with norm 8(a+b√2) = a²…

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Q: Ifx +2y+32 = x2 + 2y2 + 3z2 = x² + 2y3 + 3z3 = 2, and xx +2y2y3 +3z₂Z3 = x3x₁ +2y3v₁ +3Z3Z1 = x₁x₂ +…

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Q: QUESTION 3 Solve (by hand) the following IVP of order one on x = 0, 0.2, 1 using Euler method. If…

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Q: Let p, q be distinct primes. Show that pq is an irrational number.

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Q: (16) Prove that 22n – 1 is divisible by 3 for all n € N.

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Q: b₁ + x b₂ + x b3 + x + +x\ C₂+x, then show that A'(x) = 0 a₁ + x If A(x) = a₂ + x a3 + x C3 + x and…

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Q: t 1 (17) = { { + ¹ t 0 1 1 F(s)= = =+ = /201 5² = 1+t-e¹-2(t-e¹-¹)μ(t-1) = 1+t-e¹-2(t-et-¹)μ(t-1)…

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Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

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Q: 2. tds-t³edt 3 = when s= // (3t+1) sdt t=1

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Q: evaluate the sum of series n^2/5^n

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Q: Consider the implicitly defined function. y³ + x²y = 1 + 2x Which of the following will lead you to…

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Q: Q 3: Solve the following differential equations: A) (x + y 1)dx + (2x + 2y + 1)dy = 0. B) (x² +…

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Q: Find the value of each improper integral that converges or input divergent if it diverges. Input the…

A: Evaluation of the Integrals