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 a rectangle with sides (x+2) and (x+6), what will be the area of the small corner?EasyLevel 73If a square of side (a+b) has two equal parts besides the (a^2) and (b^2) squares, what shape are those parts?EasyLevel 73In a square visual model, one large square is divided into four parts: one square of area \(a^2\), another square of area \(b^2\), and two rectangles each of area \(ab\). Which algebraic identity does this model represent?EasyLevel 73A square model has side (2x+1). What will be its total area?EasyLevel 73If one side of a rectangle model is (t) and the other is (t+7), what will be the area?EasyLevel 73A side of a square is divided into two parts, \(a\) and \(b\). Its area model contains \(a^2\), \(b^2\), and two rectangles of area \(ab\). Which identity does this diagram represent?EasyLevel 73In a square of side (q+8), what is the area of each of the two equal rectangles?EasyLevel 73If a visual square is made for (z^2-12z+36), what will be its side?EasyLevel 73Which algebraic expression is represented by a visual area model that divides a large square into one \(x^2\) square, two \(xy\) rectangles, and one \(y^2\) square?EasyLevel 73Why does the middle term not remain in a rectangle with sides (a+2) and (a-2)?EasyLevel 73If the total area of a square model is (x^2+14x+49), what is the side of the small corner?EasyLevel 73In a model, the remaining area is (s^2-25). It can be the difference of which big and small squares?EasyLevel 73In a square with side (3x+2), what is the area of the small corner?EasyLevel 73A rectangular area model is divided into four parts with areas \(x^2\), \(3x\), \(2x\), and \(6\). Which factorised expression does this model represent?EasyLevel 73If the visual expansion of a square is (w^2+6w+9), what will be the outer side?EasyLevel 73A rectangle has length (2a+1) and breadth (a). What is the expansion of its area model?EasyLevel 73In a square with side (x-2), what will be the total area of the middle part?EasyLevel 73In a difference of squares model, if the big square has side (9) and the small square has side (2), what is the remaining area?EasyLevel 73If an area model has four regions with areas \(x^2\), \(xy\), \(xy\), and \(y^2\), and together they form one large square, which identity does the model represent?EasyLevel 73If the (a^2-b^2) model is rearranged into a rectangle, what will the rectangle area remain equal to?EasyLevel 73