expression represents the area of Dylan’s room
<h3><u>
Solution:</u></h3>
Given that,
Length of room = ![x^2 -2x+8](https://tex.z-dn.net/?f=x%5E2%20-2x%2B8)
Width of room = ![2x^2 + 5x - 7](https://tex.z-dn.net/?f=2x%5E2%20%2B%205x%20-%207)
To find: Expression that the area (lw) of Dylan’s room
Since bedroom is generally of rectangular shape, we can use area of rectangle
<em><u>The area of rectangle is given as:</u></em>
![\text {area of rectangle }=\text { length } \times \text { width }](https://tex.z-dn.net/?f=%5Ctext%20%7Barea%20of%20rectangle%20%7D%3D%5Ctext%20%7B%20length%20%7D%20%5Ctimes%20%5Ctext%20%7B%20width%20%7D)
Substituting the given expressions of length and width,
![area = (x^2 -2x+8)(2x^2 + 5x - 7)](https://tex.z-dn.net/?f=area%20%3D%20%28x%5E2%20-2x%2B8%29%282x%5E2%20%2B%205x%20-%207%29)
We multiply each term inside first parenthesis with each term inside the second parenthesis.
So it becomes,
![2x^4 + 5x^3 - 7x^2 -4x^3 -10x^2 +14x +16x^2 +40x - 56](https://tex.z-dn.net/?f=2x%5E4%20%2B%205x%5E3%20-%207x%5E2%20-4x%5E3%20-10x%5E2%20%2B14x%20%2B16x%5E2%20%2B40x%20-%2056)
Now combine like terms,
![2x^4 + x^3 - x^2 +54x - 56](https://tex.z-dn.net/?f=2x%5E4%20%2B%20x%5E3%20-%20x%5E2%20%2B54x%20-%2056)
Thus the above expression represents the area of Dylan’s room
Step-by-step explanation:
2250mg = 2250/1000 = 2.25g
59.4kilolitres = 59.4 ×1000 = 59400litres
0.000072g = 0.000072x 1000000 = 72micrograms
3.98 x 10^6 in = 3.98 × 10^6 × 25.4 × 10^-6 = 1.01092 × 10^2 km
or
3.98 × 10^6 m = 3.98 × 10^6 × 10^-3 = 3.98 × 10^3