how do you squart the middle term of 3 consecutive integers

Question

5,6,7, square the middle term

 

Answer 1

This is good to remember both ways:

 

With three consecutive integers, (x-1), x, and (x+1):

     (x-1)*(x+1) = x² - 1       [use F-O-I-L

 

That means that, for the integers 5, 6, and 7:

     5 * 7 = 6² - 1 = 36 - 1

 

And, x² = (x-1)*(x+1) + 1

 

So,

     6² = 5*7 + 1 = 35 + 1 = 36