Using areas of squares and rectangles, show that for any positive
real numbers \(a\) and \(b\), \((a+b)^2 =
a^2+2ab+b^2\).
The identity above is true for any real numbers, not necessarily
positive, in fact in order to prove it the usual way one only needs to
remember that multiplication is commutative and the distributive
property of addition and multiplication:
\(a\times b = b\times a\);
\((a+b)\times c = a\times c + b\times c\).