Take the numbers 4 and 7.

Question

If we square them we get 16 and 49, which added together becomes 65.

If we add 4 and 7 together first and then square we get 121.

The difference is 56. PROVE that there is a connection between the product of 4 and 7 and 56 FOR ANY PAIR OF NUMBERS YOU SELECT.

Answer 1

Take the numbers a and b.

If we square them we get a² and b², which added together becomes a²+b².

If we add a and b together first and then square we get (a+b)².

The difference between (a+b)² and a²+b² is....

Expand and subtract.

Answer 2

is it
a²+b²+2ab-a²+b²

2b²+2ab

if not please help

thanks

Answer 3

or is it
a²+b²+2ab-a²-b²

2ab

Answer 4

That's correct! (the last version).

Answer 5

thanks so much

Answer 6

You're welcome!