Question

1. what is the area of the following rectangle? 2x + 5 3x + 1

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the product of its length and width, i.e., \( A = \text{length} \times \text{width} \). Here, the length is \( 2x + 5 \) and the width is \( 3x + 1 \). So we need to calculate \( (2x + 5)(3x + 1) \).

Step2: Expand the product using the distributive property (FOIL method)

First, multiply the First terms: \( 2x \times 3x = 6x^2 \).
Then, multiply the Outer terms: \( 2x \times 1 = 2x \).
Next, multiply the Inner terms: \( 5 \times 3x = 15x \).
Finally, multiply the Last terms: \( 5 \times 1 = 5 \).

Now, combine like terms: \( 6x^2 + 2x + 15x + 5 = 6x^2 + 17x + 5 \).

Answer:

The area of the rectangle is \( 6x^2 + 17x + 5 \).