We can show that 14^2 = 196 by considering the area of a 14 by 14 square:
We can show that (x + 1)^2 \equiv x^2 + 2x + 1 by considering the area of an (x + 1) by (x + 1) square:
Show in a similar way that (x + 2)^2 \equiv x^2 + 4x + 4.
Then use the same method to evaluate (x + 3)^2 and (x + a)^2.
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?