Question

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? A. (x2 + 7x + 3) square inches B. (9x2 + 59x + 33) square inches C. (x2 + 3x + 7) square inches D. (9x2 + 33x + 59) square inches

Answer 1

The trim is the frame minus the glass.

`A = (5x+3)(x+6) - (4x^2 + 26x + 15)`

`= 5x^2+33x+18 - 4x^2 -26x - 15`

`=x^2+7x+3`

Answer: Choice A

Answer 2

Answer with Step-by-step explanation:

A window frame has a length of (5x + 3) inches and a width of (x + 6) inches.

Area of window frame=(5x+3)(x+6)

= 5x(x+6)+3(x+6)

= 5x²+30x+3x+18

= (5x²+33x+18) square inches

area of the glass in the window is (4x² + 26x + 15) square inches.

Area of trim around the glass=Area of window frame-Area of glass

= 5x²+33x+18-(4x²+26x+15)

=5x²-4x²+33x-26x+18-15

=(x²+7x+3) square inches

Hence, Correct option is:

A. (x² + 7x + 3) square inches