# Examples with Mathspeak

### Compute Area of House

First find the area of the square in square feet. $\begin{array}{ccc}\hfill A& =& {s}^{2}\hfill \\ & =& {\left(2x\right)}^{2}\hfill \\ & =& 4{x}^{2}\hfill \end{array}$

Then find the area of the triangle in square feet. $\begin{array}{ccc}\hfill A& =& \frac{1}{2}bh\hfill \\ & =& \frac{1}{2}\left(2x\right)\left(\frac{3}{2}\right)\hfill \\ & =& \frac{3}{2}x\hfill \end{array}$ Next find the area of the rectangular door in square feet. $\begin{array}{ccc}\hfill A& =& lw\hfill \\ & =& x\cdot 1\hfill \\ \hfill & =& x\hfill \end{array}$

### Difference of Squares

$\begin{array}{ccc}\hfill \left(x+1\right)\left(x-1\right)& =& {x}^{2}-x+x-1\hfill \\ & =& {x}^{2}-1\hfill \end{array}$

The middle term drops out, resulting in a difference of squares. $\begin{array}{ccc}\hfill \left(x+5\right)\left(x-5\right)& =& {x}^{2}-25\hfill \\ \hfill \left(x+11\right)\left(x-11\right)& =& {x}^{2}-121\hfill \\ \hfill \left(2x+3\right)\left(2x-3\right)& =& 4{x}^{2}-9\hfill \end{array}$