Divisible expression
Can you show this algebraic expression is divisible by 4?
Age
14 to 16
Challenge level
Problem
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.
Student Solutions
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