A carpenter is putting a skylight in a roof. If the roof measures 4x + 5 by 7x + 7 and the skylight measures 10x + 10 by 2x + 6, what is the area of the remaining roof after the skylight is built. Put your answer in factored form.

Answer 1

(4x + 5)(7x + 7) = 28x^2+63x+35
(10x+10)(2x + 6) = 20x^2+80x+60
---------------subtract----------
8x^2 -17 x -25 = remaining roof
which is
(8x-25)(x+1)