A.6.8.2 Drawing Diagrams to Represent More Products

Applying the distributive property to multiply out the factors of, or expand, 4(x + 2) gives us 4x + 8, so we know the two expressions are equivalent. We can use a rectangle with side lengths (x + 2) and 4 to illustrate the multiplication. Draw a diagram to show that n(2n + 5) and 2n2 + 5n are equivalent expressions.

For each expression, use the distributive property to write an equivalent expression. If you get stuck, consider drawing a diagram. a. 6(n + 2) b. p(4p + 9) c. 5r(r + ) d. (0.5w +7)w