Difference of two squares; completing the square; difference of two cubes

squarediff00

The picture above shows why a2−b2=(a+b)(a−b)



square of a plus b

This shows why (a+b)2 = a2+2ab+b2

Also why (a+b)2 ≠ a2+b2

and why √(a+b) ≠ √a+√b



Completing_the_square.ogv

This picture (above) is “completing the square” in algebra, translated into geometry.



And this little video (above) shows the difference of two cubes

A3−B3=(A−B)(A2+AB+B2)