Question

Factorise fully, (n^2 - a^2) - (n - a)^2 and explain why its always an even integer.

Answer 1

\[(n ^{2}-a ^{2})-(n-a)^{2}\]
\[(n+a)(n-a)-[(n-a)(n-a)]\]
\[(n+a)(n-a)-(n-a)(n-a)\]
\[(n-a)[(n+a)-(n-a)]\]
\[(n-a)[n+a-n+a]\]
\[(n-a)(2a)\]
\[2an-2a ^{2}\]
This is the full factorized part I think.
I am not sure about why there should always be an even integer though..

Answer 2

Thanks vengance, I understand it now :)!

Answer 3

2(an -a^2) --> 2 times an integer is the format of an even number.

Answer 4

Thanks directrix :)

Answer 5

Glad to help.