A machinist is programming a CNC machine to cut out a metal bracket. The area of the bracket is modeled by the algebraic expression ${}196m^2 - 25n^2$. To simplify the programming logic, the machinist needs to enter this expression in its factored form. Recognizing this as a difference of squares, which of the following represents the correct factored form of the expression?

A carpenter is designing a custom tabletop where the total surface area is represented by the expression ${}196m^2 - 25n^2$. To determine the side lengths for fabrication, the carpenter factors this expression into two linear binomials. If one side length is $(14m + 5n)$, the other side length must be ____.

A shop supervisor is training a new apprentice to read blueprints where areas are expressed in factored forms. For the expression ${}196m^2 - 25n^2$, the supervisor asks the apprentice to identify the components based on the difference of squares pattern $a^2 - b^2 = (a - b)(a + b)$. Match each mathematical term or factor with its correct role in the factoring process.

A production technician is configuring a laser-cutting machine to process a metal plate. The area of the plate is represented by the algebraic expression ${}196m^2 - 25n^2$. To properly input the dimensions into the machine's control software, the technician must factor this expression using the difference of squares pattern. Arrange the following steps in the correct order to complete the factoring process.

In a manufacturing specification for a steel plate, the surface area is represented by the algebraic expression ${}196m^2 - 25n^2$. True or False: The correctly factored form of this expression is ${}(14m - 5n)(14m + 5n)$.

Facilities Layout Design

Legacy Panel Specifications Conversion