Question

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 (3xy)(7xy2),where y represents the number of white tiles.
Write a simplified expression represents the number of colored tiles used for a path of length x feet?

Answer 1

they give you an expression for the number of tiles in terms of x and y, and are asking for the simplified expression.

the expression is (3xy)(7xy2).

start by multiplying the coefficients (3 * 7).

then multiply the x terms. recall that for multiplying expressions w/ the same base, you keep the base and add the exponents. when there's no exponent written, it's implied to have an exponent of 1. so you essentially have x^1 * x^1, which, using our previous rule, is x^(1+1) or simply x^2. repeat this logic with the y terms. finally, combine your coefficient, x term, and y term together.