"All limits, especially national ones, are contrary to the nature of mathematics… Mathematics knows no races… For mathematics the whole cultural world is a single country" – David Hilbert, the foremost mathematician of the 20th century, speaking as the Nazis neared power in his native Germany.

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

The picture above shows why a^{2}−b^{2}=(a+b)(a−b)

This shows why (a+b)^{2} = a^{2}+2ab+b^{2}

Also why (a+b)^{2} ≠ a^{2}+b^{2}

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