The picture above shows why a2−b2=(a+b)(a−b)
This shows why (a+b)2 = a2+2ab+b2
Also why (a+b)2 ≠ a2+b2
and why √(a+b) ≠ √a+√b
This picture (above) is “completing the square” in algebra, translated into geometry.
And this little video (above) shows the difference of two cubes