The sum of the squares of two numbers is 256 and the square of their sum is 784. What is the product of the two numbers?

So

x² + y² = 256  

And

(x + y )² = x² + 2xy + y² =  784

So

x² + 2xy + y² =  784

And

x² + y² = 256

And subtracting the second equation from the first, we have

2xy = 528     and dividing by 2 on both sides, we have

xy = 264   ....and that's the product of the two numbers

a² + b² = 256  

(a+b)² = 784  

Now (a+b)² = a² + b² +2ab  so 784 = 256 +2ab

2ab = 784 - 256 = 528

ab = 528/2 = 264