Question

A

- FRAME Hugo is designing a frame as shown at the right.
The frame has a width of x inches all the way around. Write an expression that represents the total area of the picture and frame.

Answer 1

4x^{2}+72x+320

Step-by-stepStep-by-stepStep-by-step explanation:

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Answer 2

The total area is 4
`x^(2)` + 64x + 320 square inches.

The total area of the picture and frame is 20 inches by 16 inches.

To write an expression that represents the total area, we can use the following steps:

Find the dimensions of the framed picture. The width of the framed picture is equal to the width of the picture plus twice the width of the frame. So, the width of the framed picture is 20 + 2x inches. The height of the framed picture is equal to the height of the picture plus twice the width of the frame. So, the height of the framed picture is 16 + 2x inches.

Calculate the area of the framed picture. The area of a rectangle is equal to the length times the width. So, the area of the framed picture is (20 + 2x)(16 + 2x) square inches.

Simplify the expression. We can simplify the expression by expanding the parentheses and combining like terms. This gives us the following expression:

(20 + 2x)(16 + 2x) = 320 + 64x + 4
`x^(2)`

Therefore, the expression that represents the total area of the picture and frame is 4
`x^(2)` + 64x + 320 square inches.