Answer:
Option 1 - [tex](8x^2y^2)(3xy)=24x^3y^3[/tex]
Step-by-step explanation:
Given : A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule
[tex](8x^2y^2)(3xy)[/tex] where y represents the number of white tiles.
To find : Which simplified expression represents the number of colored tiles used for a path of length x feet?
Solution :
The number of colored tiles needed to make is [tex](8x^2y^2)(3xy)[/tex]
Where, y represents the number of white tiles.
x represents the length of path in feet.
Simplifying the expression,
[tex](8x^2y^2)(3xy)[/tex]
[tex]=8\times 3\times x^2\times x\times y^2\times y[/tex]
We know, [tex]a^m\times a^n=a^{m+n}[/tex]
[tex]=24x^3y^3[/tex]
Therefore, Option 1 is correct.
