Distributive Property Area Model: Multiply 15(2b + 3c + 4d)

Published on March 12, 2026

Pre-Algebra

Learn to multiply a monomial by a trinomial using the area model to find the partial products (30b, 45c, 60d) and the final sum (30b + 45c + 60d).

Question

Here is the step-by-step solution using the area model to multiply

The area model requires multiplying the term outside the parenthesis (15) by each term inside the parenthesis (

, and

). These results are the partial products, which correspond to the areas of the three rectangles in the model.

Step 1: Find the partial products.

The partial products to fill in the boxes in the area model are

, and

Step 2: Write the product.

The product

is the sum of the partial products:

This is an application of the Distributive Property.

Final Answer Formatting:

The partial products (filling the boxes in the diagram, from left to right) are

, and

The final product is: