If n is an integer prove (n+3)^(2)-n^(2) is never even.

Let us begin by simplifying the expression:(n+3)2 - n2 = (n+3)(n+3) - n2= n2 + 6n + 9 - n2 (expanded brackets)= 6n + 9 (collected like terms)= 3(2n+3) (taken out a factor of 3)Now we can consider this simpler equivalent expression.3 is an odd number2n is even thus 2n+3 is odd (even plus odd is always odd)so we have an odd*odd which is always odd, thus never even and we are done.

HK
Answered by Hugh K. Maths tutor

6099 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would I differentiate y = 3xy + 2x^2 + x^2y^2 ?


A curve is given by the equation y = (1/3)x^3 -4x^2 +12x -19. Find the co-ordinates of any stationary points and determine whether they are maximum or minimun points.


f ( x ) = 2 x ^3 − 5 x ^2 + ax + a. Given that (x + 2) is a factor of f ( x ), find the value of the constant a. (3 marker)


Intergrate 8x^3 + 6x^(1/2) -5 with respect to x


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