Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Prove that the square of an odd number is always 1 more than a multiple of 4.
Input note: use 2n +1 as your odd number, and leave your answer in the form
4(...) +1
(4 marks)

Sagot :

birronbaronbasdnaym

Answer:

See explanation.

Step-by-step explanation:

If the odd number is 2n+1 note that n can be any number because any even number plus one will be odd. Let's start by squaring 2n+1 to get:

[tex]4n^2+4n+1[/tex]

Consider xy (x times y). xy is a multiple of both x and y because xy/x = y and xy/y = x. So it doesn't matter what n is it will be a multiple of 4. So now we know that 4n^2 and 4n are both multiples of 4. If we add them together, it will still be a multiple of 4. 2x + 4x = 6x and 6x is still divisible by x.

Now the plus 1 will always make it so it will be one more than a multiple of 4.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.