Explanation vs Derivation Math Example 3

Solution

1. 1
   Think geometrically: $(a+b)^2$ is the area of a square with side $a+b$.
2. 2
   Subdivide: top-left is $a \times a = a^2$; bottom-right is $b \times b = b^2$; the two remaining rectangles each have dimensions $a \times b$, contributing $2ab$.
3. 3
   The $2ab$ cross-term comes from these two rectangular regions — it cannot be zero unless $a=0$ or $b=0$.