Geometric Proof of $a^2-b^2=(a+b)(a-b )$ and its applications I am teaching a student on the subject of factoring. One commonly used formula is $a^2-b^2=(a+b)(a-b) $. It is easy to prove it from RHS to LHS algebraically, but how to prove it geometrically? I would also like to find some of its applications, such as this:$(\sin\theta)^2+(\cos\theta)^2=( \cos \theta +i\sin \theta)(\cos\theta -i\sin \theta )=e^{i\theta}\cdot e^{-i\theta  } =e^0=1$
Are there any other good examples?
EDIT: some comments for applications
(Albus) $\frac{1}{\sqrt a+b}=\frac{\sqrt a-b}{a-b^2}$
(Paul) $a\times b=(\frac{a+b}{2})^2-(\frac{a-b}{2})^2$
(other ) $x=x’+y’, y=x’-y’, xy=x’^2-y’^2=1$ Hyperbola  equation

Hint:
$$a^2 - b^2 =  (a-b)b + (a-b)b + (a-b)^2 $$
$$ = (a-b)[b + b + (a-b)] $$
or
$$a^2 - b^2 =  (a-b)a + (a-b)b$$
$$ = (a-b)(a+ b) $$
Draw two squares inside each other ($a>b$) and look at the three or two leftover rectangular areas.
