Prove that the difference of squares of two odd integer multiples of 3 is divisible by 72.

Q: Prove that the difference of squares of any two odd numbers is multiple of 8. (SOlve this task…

A: To proveDifference of squares of any two odd numbers is multiple of 8.

Q: Show that x60 can be computed with only seven multiplication operations.

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Q: Can someone answer all of these polynomials?

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Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

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Q: how many roots does -2x^(2)+8x^(9)-10x^(5)+12 have?

A: Roots of a polynomial are determined by its degree. Degree = highest power of x in the given…

Q: Are all perfect squares divisible by 2

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Q: Show that (2x+7) is a factor 2x2+5x2-11x-14.Hence factories the given expression completly ,by using…

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Q: Find two positive integers such that the sum of the first number and five times the second number is…

A: Solution

Q: Find three consecutive integers Such thate Hour times the sauare Of theo third less three times the…

A: Let consecutive integers are x-1,x,x+1

Q: - Find two positive even consecutive integers such that the square of the smaller integer is 10 more…

A: Consider the first even positive integer be 'x'. The second consecutive even positive integer be…

Q: Write the fourth term of the expansion of (2x+ 3y)°.

A: We can get desired result by two ways. One is by opening binomial expansion then getting fourth…

Q: Suppose, and no are the smallest of two positive integers so that 300x is a perfect square and 300y…

A: The given problem is to find the values of x and y and sum of value of x+y for which smallest…

Q: Show that (x-y) is a factor of (x2-7x2+14x-8) ,ccplete factors od expression

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Q: In a 2° factorial experiment with two factors A and B and three replicates, the contrast of factor A…

A: Given:  2^2 factorial experiment with two factors A and B  with 3 replicates and contrast of A is…

Q: Three possible products whose factors multiply to  − 2 are

A: Consider x, y, and z as the three factors of the product -2. The possible values for the three…

Q: Find the least common multiple of the denominators of 1/ (x2 - 1)  and 3/ (x2 + 4x + 3)

A: Given: 1x2-1 and 3x2+4x+3

Q: Find a counterexample to the statement that every positive integer can be written as the sum of the…

A: Claim: Every positive integer can be written as the sum of the squares of three integers. The given…

Q: Show that n2-1 is division by 8, if n is an odd positive integer

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Q: Expand and simplify using Binomial Theorem : ( 2a / 5 - 10b)^4

A: Given:  ( 2a / 5 - 10b)^4 Expand and simplify

Q: what is the largest integer less then square root of 375

A: Largest integer less than square root of 375

Q: 444...4 - 888...8 D 2.142 Show that a number 20 digits 10 digits is the square of some natural…

A: Applying sum formula of GP series.

Q: Prove by contradiction that there is no greatest multiple of 5.

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Q: If x is an integer, what is the greatest value of x which satisfies 5 < 2x + 2 < 9?

A: First of all, consider the definition of an integer. An integer is defined as the whole…

Q: 6. Estimate V55 to one decimal place by using perfect squares. Verify your answer.

A: Please see the explanation below

Q: How to simplify radicals that are not perfect squares?

A: A radical expression is one which contains a root (square root, cube root, etc.).

Q: Multiply three consecutive integers together and then add the second integer to that product. Use…

A: Consider three consecutive numbers x, (x+1), (x+2). Take a product of these numbers we get,…

Q: 1. Find two consecutive even integers whose product is 168.

A: Find two consecutive even integers whose products is 168.     Here i attached the solution of this…

Q: All perfect squares are divisible by 2. A.) True B.) False, counterexample of 16 C.) False,…

A: Numbers that are divisible by 2 are {0,2,4,6,8 ,10 } Perfect sq 1X1=1 2X2=4 3X3=9  4X4=16 5X5=15…

Q: Prove: The product of 2 numbers is equal to the product of their least common multiple and their…

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Q: if two even integers are multiflied, then the product is also even

A: Ans. True

Q: Show that 2^n >n^2 if n is large enough.

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Q: The sum of the squares of two odd integers is 1) Perfect 2) Prime 3) Not perfect

A: We will find out the required solution.

Q: Show that the sum of the squares of the first n natural numbers is given by,S=(n(n+1)(2n+1))/6

A: We have to show that the sum of the squares of the first n natural numbers is given by S=nn+12n+16…

Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers

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Q: divisible by 3

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Q: Which integers are quadratic residues of 11?

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Q: What are three possible products whose factors multiply to -2

A: To find  The three possible product whose factors are multiply to -2.

Q: (a) Factorise z6 + 1 over the real numbers.

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Q: is a factor of 2 + 5z2 – 5x +1. - O I+1 O 2z +1 O +2 O 2x -1

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Q: Prove that 13,050.046 is not the square of a natural number.

A: Use the fact that an even number is perfect square the number is divisible by 4

Q: "There is no largest integer."

A: Given: To explain the given statement as follows,

Q: How many integer solutions are there to 1 +X2+X3+X4+Xs=31 with

A: Given, x1+x2+x3+x4+x5=31 Number of Solutions when xi≥0 and xi>0.

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: Which of the following represents the square root of the quotient of the product of 64 and 5, and…

A: here, we have to Which of the following represents the square root of the quotient of the product of…

Q: If the polynomials f1 and f2 are not divisible by the polynomial g, can their sum f1 + f2 be…

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Q: the student noticed that if he writes a multiplication sign between the second and third digit of…

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