Class 8 Math Case Study on Factorisation and Identities | Worksheets & Solutions

The school intends to partition a large rectangular section of the auditorium to create a rehearsal space and a storage bay using removable panels. The partitioned rectangle’s length (parallel to the stage) is modelled by \((3a+2)\) metres and its width (perpendicular to the stage) by \((a-2)\) metres, where \(a\) is a positive integer representing the number of standard panel modules available. Inside this rectangle the team will remove a smaller rectangular storage footprint of dimensions \((a+1)\) by \((a-2)\) metres to be used as a locked store; the remaining region will be covered with acoustic panels. The project requires the students to compute total area, the net panel-covered area after removing storage, use identities to compute differences between squared dimensions when ordering square acoustic mats, and to re-evaluate material requirements when modular changes occur (for example, if the length is decreased by one module and the width increased by three modules). The work emphasises choosing the appropriate factorisation strategy (common factor extraction, grouping) and applying standard identities such as \((x+y)^2\), \((x-y)^2\), and \((x+y)(x-y)\) to simplify algebraic expressions arising in budgeting and ordering. Students must also perform sanity checks by substituting integer values of \(a\) to confirm algebraic results correspond to feasible quantities of panels.