Chapter P.4, Problem 96E

HOW DO YOU SEE IT? The figure shows a large square with an area of $a^2$ that contains a smaller square with an area of $b^2$.

(a) Describe the regions that represent $a^2-b^2$. How can you rearrange these regions to show that $a^2-b^2=(a-b)(a+b)?$

(b) How can you use the figure to show that ${(a-b)}^2=a^2-2ab+b^2?$

(c) Draw another figure to show that ${(a+b)}^2=a^2+2ab+b^2$. Explain how the figure shows this.