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

Answered by James M. Maths tutor

4639 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Factorise and solve for the solutions of X in the equation X^2 + 8X +15?


Prove that 0.5757... (recurring) = 19/33. Hence, write 0.3575757... (recurring) as a fraction in its lowest terms.


Rationalise the denominator of 2/(3-sqrt(2)).


find the values of x when 3x^2 - 6x - 9


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences