Editing Difference of two squares (section)

===Difference of two consecutive perfect squares===

The difference of two consecutive [[square number|perfect square]]s is the sum of the two [[base (exponentiation)|base]]s {{mvar|n}} and {{math|''n'' + 1}}. This can be seen as follows:

<math display=block>\begin{align}
(n+1)^2 - n^2
&= ((n+1)+n)((n+1)-n) \\[5mu]
&= 2n+1.
\end{align}</math>

Therefore, the difference of two consecutive perfect squares is an odd number. Similarly, the difference of two arbitrary perfect squares is calculated as follows:

<math display=block>\begin{align}
(n+k)^2 - n^2
&= ((n+k)+n)((n+k)-n) \\[5mu]
&= k(2n+k).
\end{align} </math>

Therefore, the difference of two even perfect squares is a multiple of {{math|4}} and the difference of two odd perfect squares is a multiple of {{math|8}}.