4.04 The distributive law
Interactive practice questions
Use the given rectangle to demonstrate the distributive property geometrically.
Complete the table below by entering the areas of the two smaller rectangles:
| Rectangle $A$A | Rectangle $B$B | |
| Area | $\editable{}$ | $\editable{}$ |
Notice that we can combine the two rectangles $A$A and $B$B to form one large rectangle. Write an expression for the area of this large rectangle using your answers from part (a).
Notice that the total length of the bottom side is $m+n$m+n. Write an expression for the area of the total rectangle using this side length.
In part (b) and (c), we found expressions which both represent the area of the larger rectangle. We have now shown that: $\editable{}+\editable{}=\editable{}\left(\editable{}+\editable{}\right)$+=(+)
A rectangle has been divided into two smaller regions.
We will use it to show the Distributive Property geometrically.
Expand the expression $5\left(s+7\right)$5(s+7).
Expand the expression $9\left(5+w\right)$9(5+w).