n is an integer greater than 1. Prove algebraically that n^2 – 2 – (n – 2)^2 is always an even number.

1) Expand the brackets: (n-2)2 = (n-2)(n-2) = n2 - 2n - 2n +4 = n2 - 4n + 42) Substitute this into the original expression: n2- 2 - (n2 - 4n +4) = n2 - 2 - n2 + 4n - 4 = 4n - 6 3) Reduce this: 4n - 6 = 2(2n - 3)4) Conclusion: This is always an even number as for all values of n the expression is a multiple of 2

JM
Answered by James M. Maths tutor

4874 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

What is the square root of (2^6 + 6^2)


What is 12x^6 / 7 divided by 4x^2 / 5 ?


A 20-foot ladder is leaning against a vertical wall. The bottom of the ladder is pulled away horizontally from the wall at 3 feet per second. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is 10 feet away?


A right-angled triangle has side lengths of 8.65cm and 10.15cm. What is the length of its hypotenuse?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences