The problem asks us to use each expression to calculate the number of tiles an employee must add to squares with side lengths of 135 tiles to create the next design.

Let's analyze each expression and substitute $n = 135$ to find the number of tiles for each employee.

Expressions:

1. Wilma's Expression: $4n + 4$
2. Howard's Expression: $2(n + 2) + 2n$
3. Tyler's Expression: $n + n + n + n + 4$ or simplified as $4n + 4$
4. Tamara's Expression: $(n+2)^2 - n^2$

Calculations:

Now we will substitute $n = 135$ into each expression.

1. Wilma's Expression:
   $4n + 4 = 4(135) + 4 = 540 + 4 = 544$

2. Howard's Expression:
   $2(n + 2) + 2n = 2(135 + 2) + 2(135) = 2(137) + 270 = 274 + 270 = 544$

3. Tyler's Expression:
   $n + n + n + n + 4 = 4n + 4 = 4(135) + 4 = 544$

4. Tamara's Expression:
   $(n+2)^2 - n^2 = (135+2)^2 - 135^2 = 137^2 - 135^2$

   Calculating $137^2$ and $135^2$:

   $137^2 = 18769, \quad 135^2 = 18225$

   So,

   $137^2 - 135^2 = 18769 - 18225 = 544$

Conclusion:

All four expressions yield the same result of 544 tiles when $n = 135$.

Would you like more details on the calculations, or do you have any questions?

Related Questions:

1. What is the difference between an expression and an equation?
2. How do we simplify algebraic expressions with parentheses?
3. Can you explain how to calculate the square of a binomial expression?
4. What are some methods for verifying the equality of two expressions?
5. How can algebra be used to model real-world problems?

Tip:

When verifying multiple expressions, always check if they simplify to the same form or if they produce the same result when substituting the given values.