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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
Answer
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 (
Step 1: Find the partial products.
-
First rectangle (under
):
Multiplyby : -
Second rectangle (under
):
Multiplyby : -
Third rectangle (under
):
Multiplyby :
The partial products to fill in the boxes in the area model are
Step 2: Write the product.
The product
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
The final product is: