Question

a regular pentagon has a side length of y - 3.
a regular heptagon has a side length of 15 - y.
the difference between the perimeters of the two shapes is represented by the expression:
5(y - 3) - 7(15 - y)
write an expression equivalent to 5(y - 3) - 7(15 - y) using the fewest possible terms.
show all work neatly and clearly.

Explanation:

Step1: Apply distributive property

First, distribute the 5 and -7 to the terms inside the parentheses. For \(5(y - 3)\), we get \(5\times y - 5\times3 = 5y - 15\). For \(-7(15 - y)\), we get \(-7\times15 + (-7)\times(-y)= - 105 + 7y\). So the expression becomes \(5y - 15 - 105 + 7y\).

Step2: Combine like terms

Now, combine the \(y\)-terms and the constant terms. The \(y\)-terms are \(5y\) and \(7y\), so \(5y + 7y = 12y\). The constant terms are \(-15\) and \(-105\), so \(-15-105=-120\). Putting it together, we have \(12y - 120\).

Answer:

\(12y - 120\)