If the area of Bianca’s rectangular backyard patio is represented by the expression x2 – 18x + 81, and the length of the patio is represented by the expression x − 9

:

1. what is the expression for the width of the patio? Explain and show all work.

2. what special rectangular shape is the patio? (can be determined by side lengths). Explain and show all work.

9, square

Step-by-step explanation:

1) factor x^2-18x+81 to get answer

x^2-9x-9x+81

x(x-9) -9(x-9)

(x-9) (x-9)=0

x-9=0

x=9

the width is 9

since both the length and width is 9, this is a square

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)