Question

use the area model to find the product (x - 4)(2x + 1). first, find the partial products. 2x 1 x 3x 1 -4 -8x -4 now, write the product. simplify your answer. (x - 4)(2x + 1) =

Explanation:

Step1: Identify Partial Products

The partial products from the area model are \( 2x \cdot x = 2x^2 \) (wait, the yellow box was mislabeled, correct is \( x \cdot 2x = 2x^2 \)), \( x \cdot 1 = x \), \( -4 \cdot 2x = -8x \), \( -4 \cdot 1 = -4 \). Wait, the given yellow box has \( 3x \) which is wrong, correct first partial product is \( 2x^2 \). Let's use correct partial products: \( 2x^2 \), \( x \), \( -8x \), \( -4 \).

Step2: Combine Like Terms

Combine \( x \) and \( -8x \): \( x - 8x = -7x \). Then add \( 2x^2 \), \( -7x \), and \( -4 \). So \( 2x^2 - 7x - 4 \). Wait, let's redo with correct initial partial products. Wait, the area model: top row is \( 2x \) and \( 1 \), left column is \( x \) and \( -4 \). So the four rectangles:

1. \( x \times 2x = 2x^2 \) (yellow)
2. \( x \times 1 = x \) (teal)
3. \( -4 \times 2x = -8x \) (orange)
4. \( -4 \times 1 = -4 \) (pink)

Now sum all partial products: \( 2x^2 + x - 8x - 4 \).

Step3: Simplify Like Terms

\( x - 8x = -7x \), so \( 2x^2 - 7x - 4 \).

Answer:

\( 2x^2 - 7x - 4 \)