A construction site supervisor is measuring a square area where a new foundation will be poured. The area of the square is represented by the expression ${}16z^2 - 72z + 81$. Since the area of a square is the square of its side length, which binomial represents the side length of this foundation?

A software developer is writing an algorithm to automatically factor quadratic cost models for a corporate finance department. To ensure the program correctly applies the perfect square trinomial formula to the specific cost model ${}16z^2 - 72z + 81$, match each component of the cost model to its corresponding part in the general formula $a^2 - 2ab + b^2 = (a - b)^2$.

A manufacturing engineer is documenting a technical specification that uses the expression ${}16z^2 - 72z + 81$. To make the manual easier to read, the engineer states that this expression is a perfect square trinomial and can be simplified to $(4z - 9)^2$. Is the engineer's simplification mathematically correct?

An aeronautical engineer is simplifying a drag coefficient expression in a flight simulation model. The expression is given by the trinomial ${}16z^2 - 72z + 81$. The engineer recognizes that this expression can be simplified into a binomial squared to make the code more efficient. Rewrite the expression ${}16z^2 - 72z + 81$ in its factored form as a squared binomial.

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