Mathematics
Visual models of identities
सर्वसमिकाओं के दृश्य मॉडल
In Class 9 Mathematics, under the chapter Exploring Algebraic Identities, students use geometric diagrams and area-based representations to understand algebraic identities visually. They relate squares and rectangles formed from algebraic expressions to expansions such as binomial products, helping them see why both sides of an identity are equal rather than merely memorising formulas.
Practice questions
In which visual model are the two middle rectangles equal to \(ab\) and \(ab\)?EasyLevel 70A rectangle has length \(r+s\) and breadth \(r\). What will be the total area in the area model?EasyLevel 70In algebra tiles, \(x^2\) tile, \(7x\) tiles, and \(12\) unit tiles can show which area?EasyLevel 70If \((x+2)(x+3)\) is shown by a rectangle, what is the sum of its four parts?EasyLevel 70The area model of a square with side \(t+1\) leads to which result?EasyLevel 70In which model can a \(b^2\) square be removed from a corner of an \(a^2\) square and the remaining part rearranged into a rectangle?EasyLevel 70Which is the correct expansion in the area model of a square with side \(10-3\)?EasyLevel 70A square has side \(a+b+c\). In the visual model, the total area can be thought of in how many main types of terms?EasyLevel 70If a rectangle is divided into parts \(x^2\), \(4x\), \(2x\), and \(8\), what can its dimensions be?EasyLevel 70Why is \(a^2+2ab+b^2\) shown as a complete square in a visual model?EasyLevel 70Which figure most directly shows the area \((p+q)^2\)?EasyLevel 70In a diagram, two \(ab\) rectangles are added with \(a^2\) and \(b^2\) squares. What will be the total area?EasyLevel 70In the model of a square with side \(z-1\), which term remains positive?EasyLevel 70If an \(a\) by \(a\) square is joined with an \(a\) by \(b\) rectangle, how can the formed area be written?EasyLevel 70A rectangle has parts \(x^2\), \(5x\), \(x\), and \(5\). Which multiplication does it show?EasyLevel 70In which visual proof is an identity proved by writing the same area in two ways?EasyLevel 70In a square of side \(x+y\), apart from \(x^2\) and \(y^2\), which parts are obtained?EasyLevel 70If a rectangle has length \(x+4\) and breadth \(x+4\), which figure is it equivalent to?EasyLevel 70In the visual model of \((a-b)^2\), what total rectangular area is subtracted from \(a^2\)?EasyLevel 70Using the identity, what is the area of a square with side \(7+3\)?EasyLevel 70