Verify that for all n ≥ 1, the sum of the squares of the first 2n positive integers is given by the formula 12 + 22 + 32 + ··· + (2n) 2 = n(2n + 1)(4n + 1) 3

Q: Solve for u. 7 9- u+6

A: According to the question, we have to solve the expression 7u+6=-6 and find the value of u. An…

Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: In Z2, 1 + 1 + 0 + 1 = 1 and 1 + 1 + 1 + 1 = 0.

A:

Q: verify that A(B + C) = AB + AC

A: Now,

Q: Add (7x6 + 10x2 – 10) + (3x6 – 6x3 + 4). O 10x6 + 4x2 – 6 - O 10x6 + 4x3 – 6 O 10x6 – 6x3 + 10x2 – 6…

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Q: (f) The sum of the squares of the odd integers between 0 and 100.

A: Explained below

Q: find (2n +1)! = 120

A: Here we have to find the value of n.  2n+1!=120

Q: Which of the following is equivalent to (1-x)(1+x) -3x(2-x)  A. -4x2 - 6x + 1  B. 2x2 - 7x + 1 C.…

A: Given expression is (1-x)(1+x) - 3x(2-x)

Q: 22n+1 3n+1 2.

A:

Q: FIND S + 4 (s² – 8S + 6) -

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Q: 7 Find mLGBF. (4x-4)* (6x + 4)*

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Q: Find the x3 term in (x-1) (2x-2)4   4=n, 5 terms

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Q: a) 2x + 5 > 4x – 3

A:

Q: verify that 6A = 3(2A)

A: Here given  Thus

Q: Show that dx =に 3+ Vx x3/2 – 3x + 18VX- 54 In (3 + V) +C

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Q: Find the solution for 3/4 - (-6/12)

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Q: the number of nonnegative integer solutions to (x₁ + x2 + x3 + x4 + X5) (X6 + X7 + x8 + x9 + x10) =…

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Q: Prove that the expression 2y2 - 128 is equal to 2(x2+2) (x² – 2) (x³ + 4x* + 16).

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Q: Subtract (4q - 8) from the sum of (3q² – 7q – 4) and (6q² + 6q − 2).

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Q: verify that 3(A + B) = 3A + 3B

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Q: Prove that if 8x-5=-2x-15 then -x=1

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Q: The figure below shows that 4 one-inch segments are needed to make a 1 × 1 square, 12 one-inch…

A: 1×1 square require 4 one inch  segments 2×2 square require 12 one inch  segments 3×3 square requires…

Q: Find the sum of the coefficient of the variables in the expression of (2x+3y-z)8

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Q: Find all possible pairs of integers x, y so that 7x + 3y = 4. Then find which of these pairs makes…

A: Given:   7x+3y=4                        ........(1) We have to find all possible pairs of integers…

Q: Find (1 + i)10.

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Q: Prove they are equal 4 = 7(2x+ 1) - 5x -3(3x + 1)

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Q: Indicate the least integer n for which (3x⁰+2x²)(x³ +3x) x+14x € 0(x¹).

A: Given: 3x6+2x2x3+3xx4+14x∈Oxn To find: Least integer n for which the given condition holds.

Q: represent, 5 x 17=85, 5 x 29=145, 13 x 17=221 as a sum of two squares according to the formula n1 x…

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Q: Use the Binomial Theorem to simplify (x – 2)3 as a polynomial ax3 + bx? + cx + d.

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Q: Find the square root of the product of (3+ j4) and (2+ j8)

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