A carpenter is measuring a square piece of plywood with an area represented by the expression $x^2 + 14x + 49$. To factor this expression and determine the side length of the square, arrange the following steps of the factoring procedure in the correct order.

An engineering technician is verifying a mathematical model for a square component's structural load. The load distribution is represented by the perfect square trinomial pattern $a^2 - 2ab + b^2$. According to the standard factoring procedure, which of the following is the correct factored form of this expression?

A manufacturing technician is using algebraic expressions to determine the dimensions of square metal plates. Match each component of the three-step factoring procedure for perfect square trinomials to its correct rule or algebraic form.

A quality control technician is following the standard three-step procedure to factor a perfect square trinomial for a structural design formula. True or False: In the first step of this procedure, the technician can confirm the expression fits the perfect square pattern simply by verifying that the first and last terms are perfect squares.

A machinist is analyzing an algebraic expression for the area of a square machine part to determine its side length. According to the standard three-step procedure, after identifying that the first term is $a^2$ and the last term is $b^2$, they must verify if the middle term is exactly ____ the product of $a$ and $b$.