Question

diploma. the frame will have the dimensions shown below. write an expression to represent the area of the frame.
a. $x^2 + 10$
b. $x^2 + 7x + 10$
c.

Explanation:

Step1: Recall area of rectangle

The area of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). Here, the length of the frame is \( x + 5 \) and the width is \( x + 2 \).

Step2: Multiply the binomials

We use the distributive property (FOIL method) to multiply \( (x + 5)(x + 2) \).
First terms: \( x \times x = x^2 \)
Outer terms: \( x \times 2 = 2x \)
Inner terms: \( 5 \times x = 5x \)
Last terms: \( 5 \times 2 = 10 \)

Now, combine like terms: \( x^2 + 2x + 5x + 10 = x^2 + 7x + 10 \)

Answer:

B. \( x^2 + 7x + 10 \)