Question

can anyone be able to me with this question rq
A carpenter is putting a skylight in a roof. If the roof measures 10𝑥 + 8 by 8𝑥 + 6 and the skylight measures 𝑥 + 5 by 3𝑥 + 4, what is the area of the remaining roof after the skylight is built?
a. 77𝑥^2 + 115𝑥 + 68
b. 77𝑥^2 + 105𝑥 + 28
c. 83𝑥^2 + 115𝑥 + 68
d. 77𝑥^2 − 105𝑥 + 28

Answer 1

Area of the roof:

Ar = ( 10 x + 8 ) ∙ ( 8 x + 6 ) = 8 x ∙ 10 x + 8 x ∙ 8 + 6 ∙ 10 x + 6 ∙ 8 =

80 x² + 64 x + 60 x + 48 = 80 x² + 124 x + 48

Area of the skylight:

As = ( x + 5 ) ∙ ( 3 x + 4 ) = 3 x ∙ x + 3 x ∙ 5 + 4 ∙ x + 4 ∙ 5 =

3 x² + 15 x + 4 ∙ x + 20 = 3 x² + 19 x + 20

Area of the remaining roof after the skylight is built:

A = Ar - As = 80 x² + 124 x + 48 - ( 3 x² + 19 x + 20 ) =

80 x² + 124 x + 48 - 3 x² - 19 x - 20 =

80 x² - 3 x² + 124 x - 19 x + 48 - 20 =

77 x² + 105 x + 28

Answer b