A:
Width of the deck = [tex]2x+3[/tex] units
Length of the deck = [tex]5x+6[/tex] units
So area of rectangular deck = Length * width
= [tex](5x+6)(2x+3)[/tex]
Area = [tex]10x^{2}+15x+12x+18[/tex]
Area= [tex]10x^{2}+27x+18[/tex] units square
As mentioned in part B, the area of the pool is [tex]3x^{2}+7x+6[/tex] so the combined area of the deck and pool is
Area = area of rectangular deck + area of pool
= [tex]13x^{2}+34x+24[/tex] unit square
B:
The area of only the deck is [tex]10x^{2}+27x+18[/tex] unit square
