Prove that (3n+1)²-(3n-1)² is a multiple of 4 taking into account that n is a positive integer value
- 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
NK
Related Maths GCSE answers
All answers ▸write 36 as a product of its prime factors
A bag contains 10 apples. Three of the apples are green and seven of the apples are red. If an apple is pulled from the bag at random, what is the probability that the apple will be green?
3x + 12 = 24, solve for x.
Factorise 12x^2 - 20x + 3