HELP PLEASE
A family is building a rectangular patio in their backyard. The rectangular yard has dimensions of (8x+2) by (6x+3) and they are planning the patio to be (x+5) by (3x+1) what is the remaining area of the yard after the patio has been built?
a. 3x^2+16x+5
b. 48x^2+36x+6
c. 51x^2=52x+11
d. 45x^2+20x+1
If you had values instead of algebraic expressions, you would find the area of the patio and subtract that from the area of the yard. Even though you don't have values, you can still find the area and subtract by expanding and simplifying: (8x + 2)(6x + 3) 8x × 6x = 48x² 8x × 3 = 24x 2 × 6x = 12x 2 × 3 = 6 So you get 48x² + 36x + 6 as your area of the yard
(x + 5)(3x + 1) x × 3x = 3x² x × 1 = x 5 × 3x = 15x 5 × 1 = 5 So the area of the patio is 3x² + 16x + 5
