A window frame has a length of (5x + 3) inches and a width of (x + 6) inches. The area of the glass in the window is (4x2 + 26x + 15) square inches. What is the area of the trim around the glass in the window?

x^2 + 7x + 3 in^2.

Step-by-step explanation:

The area of the whole frame = (5x + 3) (x + 6)

= 5x^2 + 33x + 18

So the area of the rim = 5x^2 + 33x + 18 - (4x^2 + 26x + 15)

= x^2 + 7x + 3 in^2.

The trim area is x² + 7x + 3.

Step-by-step explanation:

First determine the area of the window frame. Then subtract the given glass area. The remainder is the area of the trim.

Area of window frame: (5x + 3) (x + 6) = 5x² + 33x + 18

Area of glass; 4x² + 26x + 15

Subtracting the glass area from the frame area, we get:

x² + 7x + 3

The trim area is x² + 7x + 3.