Copyright © University of Cambridge. All rights reserved.

Show that $(1+x+y)^2-(1-x-y)^2$ is divisible by $4$ for all integer values of $x$ and $y$.

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

*This problem is taken from the UKMT Mathematical Challenges.**View the archive of all weekly problems grouped by curriculum topic*