A rectangular wooden frame has side lengths 5x and 7x+1. The rectangular opening for a picture has side lengths 3x and 5x. What is the area of the wooden part of the frame?

The area of the wooden part of the frame is 5x (4x + 1)

Step-by-step explanation: Please refer to the attached diagram.

Upon careful observation, you would notice that the diagram shows two different rectangles placed on each other.

According to the question, the rectangular wooden frame (ABCD) has sides measuring 5x and 7x + 1. Also there is a rectangular opening (EFGH) right inside the wooden frame that measures 3x and 5x.

Therefore, the shaded portion in the diagram represents the wooden part of the frame not covered by the picture.

Hence, the area of the shaded portion is given as

Area of the wooden frame ABCD minus Area of the opening EFGH

If the area of a rectangle is given as A = L × W,

Then area of ABCD = 7x + 1 (5x)

Area = 35x² + 5x

Also the area of EFGH = 5x (3x)

Area = 15x²

Area of the wooden part of the frame is given as

A = Area ABCD - Area EFGH

A = 35x² + 5x - 15x²

A = 20x² + 5x

By factorization, the right hand side of the equation becomes

A = 5x(4x + 1)

0 is its x and y coordinate