Chapter R - Section R.3 - Polynomials - R.3 Exercises - Page 31: 100

$\begin{array}{ l } \begin{array}{{l}} \mathrm{The\ equation} \ x( y+z) =xy+xz \mathrm{\space \\is\ an\ application\ of\ the\ distributive\ property\ which\ shows\ that}\\ \mathrm{the\ area\ of\ the\ largest\ rectangle\ is\ equivalent\ to\ the\ sum\ of\ the\ areas\ of\ the\ smaller\ rectangles.} \end{array} \end{array}$

$\begin{array}{ l } \begin{array}{{l}} \mathrm{The\ area\ of\ the\ largest\ rectangle\ is\ equivalent\ to\ the\ sum\ of\ the\ areas\ of\ the\ two\ }\\ \mathrm{smaller\ rectangles.From\ the\ given\ figure\ we\ can\ observe\ that\ the\ area\ of\ the\ }\\ \mathrm{largest\ rectangle\ is} \ x( y+z).\\ \\ \mathrm{The\ area\ of\ the\ larger\ figure\ is} \ xy.\ \mathrm{The\ area\ of\ the\ }\\ \mathrm{smaller\ figure\ is} \ xz.\ \mathrm{The\ sum\ of\ the\ two\ smaller\ figures\ is} \ xy\ +\ xz.\ \\ \\ \mathrm{To\ show\ that\ } \mathrm{the} \ \mathrm{area\ of\ the\ largest\ rectangle\ is\ indeed\ the\ sum\ of\ the\ two\ smaller\ rectangles} \ \\ \mathrm{we\ can\ take\ the\ expression\ for\ the\ largest\ rectangle\ and\ apply\ the\ distributive\ }\\ \mathrm{property} \ \mathrm{as\ follows} : \\ \\ \ x( y+z) \ =\ xy+xz \\ \\ \mathrm{which\ is\ equivalent\ to\ the\ expression\ }\\ \mathrm{for\ the\ sum\ of\ the\ two\ smaller\ figures.\ } \end{array} \end{array}$