Prove that (2n + 3)2 - (2n-3) is a multiple of 8using relevant method

1.	Prove that (2n + 3)2 - (2n-3) is a multiple of 8using relevant method of proof.
Answer» (2n+3)²- (2n-3)² [ (2n +3) - (2n - 3) ] [ (2n + 3) + (2n - 3) ] = [ 6 ] [ 4n ] = 24n = 8 [ 3n ] This is a multiple of 8 (2n + 3)^2 - (2n - 3)^2 = (4n^2 + 9 + 12n) - (4n^2 + 9 - 12n) = 4n^2 + 9n + 12n - 4n^2 - 9 + 12n = 24n = 8*3n Hence, on solving we get 24n which is multiple of 8

Prove that (2n + 3)2 - (2n-3) is a multiple of 8using relevant method of proof.

Answer»

(2n+3)²- (2n-3)²

[ (2n +3) - (2n - 3) ] [ (2n + 3) + (2n - 3) ] =

[ 6 ] [ 4n ] =

24n =

8 [ 3n ] This is a multiple of 8

(2n + 3)^2 - (2n - 3)^2

= (4n^2 + 9 + 12n) - (4n^2 + 9 - 12n)

= 4n^2 + 9n + 12n - 4n^2 - 9 + 12n

= 24n

= 8*3n

Hence, on solving we get 24n which is multiple of 8