Prove that (3n+1)²-(3n-1)² is a multiple of 4 taking into account that n is a positive integer value

  1. Square the brackets (3n+1)²= (3n+1)(3n+1) = 9n²+3n+3n+1 = 9n²+6n+1 (3n-1)²= (3n-1)(3n-1) = 9n²-3n-3n+1 = 9n²-6n+12. Write out the full equation (9n²+6n+1) - (9n²-6n+1) = 9n²+6n+1-9n²+6n-1 = 12n3. Explain your reasoning 12n is divisible by 4 as (12n÷4) equals 3n therefore (3n+1)²-(3n-1)² is a multiple of 4 as 4 goes into 12 a total of 3 times and 3 is an integer
Answered by Nalin K. Maths tutor

6153 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

3^2 + 4^2 = x^2. Find x


John has £385 he wants to give to Charlie, Ben and Sarah. He gives them the money in the ratio 1:2:4 respectively. How much money does each person get?


Write 0.38 as a percentage and as fraction.


A linear sequence starts a + 2b, a + 6b, a + 10b … The 2nd term has value 8 The 5th term has value 44 Work out the values of a and b.


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