Squared ‘surprises’

It doesn’t always have to be complicated, math, to be fun.

Take a number, add two to it, multiplicate these two, ad one to the stew, and you have the quadratic tern of the average of the first two numbers.
Some examples:

    \[12\cdot 14+1=168+1=169=13^2=\left(\frac{12+14}{2}\right)^2\]

Let’s do another.

    \[23\cdot 25+1=575+1=676=24^2=\left(\frac{23+25}{2}\right)^2\]

The solution is simple. Let the first number be n, the second n+2 and you get

    \[(n(n+2)+1=n^2+2n+1=(n+1)^2\]

You could also use another binomial when n is considered to be the average

    \[(n-1)(n+1)+1=n^2-1+1=n^2\]

Math always works out correct. Never surprises. Phew.