Prove that the difference of the squares of two consecutive even numbers is divisible by 4.
Write down an algebraic expression for an even number
2n
Write down the algebraic expression for the next consecutive even number after 2n
2n + 2
Write down an expression showing the difference of the squares of two consecutive even numbers
Do the larger value subtract the smaller value
Expand the brackets and collect like terms
Show that the final answer is divisible by 4 (a multiple of 4)
Do this by writing it as 4 × ... and write a conclusion that copies the wording in the question
is a multiple of 4, so the difference between the squares of two consecutive even numbers is divisible by 4