a) Explain why the multiplicativity of (n) follows from the formula p(n) = n* | (1 - 1/p) where the product runs over the prime factors of n.

Q: Multiple Choice x=25.34.113 y= 23 .11 What is the prime factorization x/y? O 23.11 O 2³ . 11? O 2…

A: Given : x = 2 6 • 3 4 • 11 3  y = 2 3 • 11  Find :  prime factorization x/y

Q: How many terms are there in the multinomial expansion of (x₁ + x₂ + ...........+xr)n?

A: Multinomial expansion :  (X1 + X2 + X3 + ......Xr)n  We have to calculate no. of terms in this…

Q: Find a formula for 1/2+1/4+1/8+.+ 1/2h by examining the values of this expression for small values…

A:

Q: Multiply: (a) (m + 2)(m – 2), (b) (3y + 4)(3y – 4), (c) (b -6 +), and (d) (tª – 6u)(tª + 6u). To…

A: To find the product of two binomials, we generally use the FOIL (First, Outer, Inner, Last) method.…

Q: 3. (a) Use the Binomial Theorem to expand and simplify (3a²-4b)6

A:

Q: (1+ 2x + 4x? +8x + ...)(3x² + 3x* + 3a° + · . .)(x³ + 2a® + 3x° +

A:

Q: What is the summation notation of this expanded form: A. (1/3)+(3/5)+(5/7)+(7/9) B. 1-4+9-16+25

A:

Q: Use the Binomial Theorem to expand and simplify (y2 -2)3 (y2+2)3.

A: Given expression is y2−23y2+23 We have to expand the expression y2−23y2+23 by using Binomial…

Q: Find the term indicated in the expansion (x + 2y)6; third term.

A: Find the term indicated in the expansion (x + 2y)6; third term.

Q: Find the sum of coefficients in the expansion (2x+1)^3 (x+2y)^4. 2610 2817 2187 2160

A: We can solve the problem by expanding this and adding them

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: Show that (a) 8n −3n is divisible by 5 for all natural numbers n.  (b) n2 −n +41 is odd for all…

A: expansion of (a+b)n = hco an bo + nc1 an-1 b1 +.......... +ncn ao b n

Q: (c) Find the term independent of x in the expansion of, 15 + 4x?

A:

Q: 1. [K5] Use long division to divide 4x* – 2x² - 1 by x – 1. Then write the associated division…

A:

Q: ) Find the coefficient of xy in the expansion of (x + y²)°. ) Find the coefficient of x5y® in the…

A:

Q: Explain why the terms of the polynomial y to the second power plus 7 are said to be relatively…

A: Two numbers are said to be relatively prime when they have no common factor except  1

Q: Find an expression, in terms of n for the coefficient of x in the expansion (1+4x) + (1+4x)² +…

A: ANSWER :

Q: 8 For which values of mis x - 1 a factor of x³ + m²x² + 3mx + 1? (a) Show that n = 1 is a root of…

A:

Q: I also found that the expression was divisible by 13 at n=6 and n=10. Is there anyway you could…

A: Any number n can be written in the form          n = 3m, or 3m+1, or 3m + 2 for some integer m.…

Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

A:

Q: Translate a of n=1/8(n-1) to a recursive formula

A:

Q: find the coefficient of t8 in expansion of 2t(3+t)20

A:

Q: Obtain the regular expressions for the following: (a) {a4n+3 : n ≥ 0} (b) {a, a4, a8, … }

A:

Q: Factorize (i) 1144 in Z (i) 1144 in Z[i] (ii) 1144 in Zp[x] where p is a Z-prime greater than 1144.

A: Given

Q: Thank you! This might be a stupid question... but how do you algebraically solve the part where you…

A: