Question

A carpenter is assigned a job of installing a spa into a pre-existing deck. The dimensions of the deck are (6x + 1) wide by (4x - 3) long. The dimensions of the spa are (4x + 5) wide by (x + 6) long.

Write the polynomial that represents the remaining area of the deck after the carpenter cut the hole out for the spa.

Answer 1

Area of the deck minus area of spa is equal to the area of the deck remaining...

A=(6x+1)(4x-3)-(4x+5)(x+6)

A=24x^2-18x+4x-3-4x^2-24x-5x-30

A=24x^2-14x-3-4x^2-29x-30

A=20x^2-43x-33 or if you factor...

A=20x^2+12x-55x-33

A=4x(5x+3)-11(5x+3)

A=(4x-11)(5x+3)