Chapter R - Review of Basic Concepts - R.3 Polynomials - R.3 Exercises - Page 34: 106

$x(y+z)=xy+xz$. See explanations.

Step 1. Based on the given conditions, the area of the left rectangle is $A_1=xy$ Step 2. The area of the right rectangle is $A_2=xz$ Step 3. The long side is $y+z$ and the area of the largest rectangle is $A_3=x(y+z)$ Step 4. The area in step 3 is the sum of the areas from the first two steps, we have $x(y+z)=xy+xz$ which geometrically support the distributive property