Question

A square photograph has a side length of x + 8. It is

surrounded by a frame that is 2 inches wide all the way
around. Write a simplified expression for the area of
just the picture frame.

Answer 1

(x + 10)^2

Explanation:

*It helps to draw a diagram for these types of questions

Side length of photograph: x + 8

Width of frame: 2 in.

Area of a square: s^2

A = ((x + 8) + 2)^2

= (x + 10)^2

Therefore the area of the photograph with the frame is (x + 10)^2

Answer 2

• 8(x + 10) or 8x + 80

Explanation:

Area of the picture:

• (x + 8)²

Side of the photograph with the frame:

• (x + 8) + 2*2 =
• x + 12

Area of the frame:

• (x + 12)² - (x + 8)² =
• (x + 12 + x + 8)(x + 12 - x - 8) =
• (2x + 20)(4) =
• 8(x + 10)

or

• 8x + 80