When two numbers are added and the sum is multiplied by half of itself, what pattern do you notice? Represent this process algebraically and prove that it equals half the square of their sum.
Answer:
Let the two numbers be \(a\) and \(b\).
Sum of the two numbers \(=\) .
Half of the sum of the two numbers \(=\)
Half of the square of the sum of the two numbers \(=\)
Thus, .