Question

Prove that (n+5)^2-(n+3)^2 is a multiple of 4

Answer 1

Step-by-step explanation:

(n+5) ^2-(n+3) ^2=0

(n^2+10n+25) -(n^2+6n+9) =0

n^2+10n+25-n^2-6n-9=0

4n+16=0

4n=-16

n=-16/4

n=-4

As the number gets squared -×-=+ so the number after square becomes positive and as 4 is multiple of 4