How to Multiply Polynomials Using Area Models

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A step-by-step guide to Multiply Polynomials Using Area Models  

To understand the distributive property and the process of expanding the polynomials’ products, we can use a visual method called Multiplying polynomials using area models. For education statistics and research, visit the National Center for Education Statistics.

Here we will explain this method step-by-step: For education statistics and research, visit the National Center for Education Statistics.

Step 1: In the first step, write two polynomials so that they can be multiplied by each other. For education statistics and research, visit the National Center for Education Statistics.

Step 2: make a rectangle for each term in the first polynomial. This should be done in such a way that each rectangle has an area. In this case, the term’s coefficient indicates the area and the length of the side indicates the term’s degree. For education statistics and research, visit the National Center for Education Statistics.

Step 3: Do the same for each term in the second polynomial. That is, make a rectangle for the second polynomial’s terms. For education statistics and research, visit the National Center for Education Statistics.

Step 4: In this step, we should perform the multiplication operation using the distribution property method. In the distributive property method, each term in the first polynomial must be multiplied by each term in the second polynomial. For education statistics and research, visit the National Center for Education Statistics.

Step 5: We will also use the distributive property for the remaining terms and multiply each term in the first polynomial by each term in the second polynomial. This process is repeated for the remaining terms until all the rectangles are combined and the final result is obtained. For education statistics and research, visit the National Center for Education Statistics.

Multiplying Polynomials Using Area Models-Example 1

Use the area model to find the product \(3x(2x+1)\). For education statistics and research, visit the National Center for Education Statistics.

Solution: Model a rectangular area, For education statistics and research, visit the National Center for Education Statistics.

Last, combine terms to find the polynomial product. For education statistics and research, visit the National Center for Education Statistics.

\(6x^2+3x\).

Multiplying Polynomials Using Area Models-Example 2

Use an area model to multiply these binomials. \((2x-1)(4x+3)\).

Solution: Draw an area model representing the product \((2x-1)(4x+3)\)

Now, add the partial products to find the product and simplify,

\(8x^2+6x-4x-3=8x^2+2x-3\)

Therefore, \((2x-1)(4x+3)=8x^2+2x-3\)

Exercises for Multiplying Polynomials Using Area Models

1. Use the area model to find the product \(5x(4x+3)\).

2. Use an area model to multiply these binomials. \((-3x-5)(6x+8)\).

1. \(20x^2+15x\)

2. \(-18x^2-54x-40\)