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 an area model, a big square is made with two parts (a) and (b). What is the area of the whole square?EasyLevel 69If the side of a square model is (x+3), what is its expanded area?EasyLevel 69In an area diagram, a strip of width (b) is removed from a big square. Which identity does this show?EasyLevel 69The area of a rectangle with sides (a+b) and (a-b) is equal to what?EasyLevel 69In a tile model, one (x^2) tile, four (x) tiles, and four unit tiles form which square?EasyLevel 69A square of side (p+q) is divided into four regions. What is the combined area of the two rectangles?EasyLevel 69In a visual model of a large square of side a, two rectangular strips of area ab are removed. The corner square of area b² is added back once because it is included in both strips. Which algebraic identity does this model represent?EasyLevel 69If a visual model has a big square of area (a^2) and a small corner of area (b^2) removed, which product can represent the remaining area after rearrangement?EasyLevel 69The side of a square is (y+5). According to the area model, what will be the middle term?EasyLevel 69A square is made from tiles representing (x^2+8x+16). What will be its side?EasyLevel 69In a rectangle model, the length is (r+2) and the breadth is (r+3). What is the total area?EasyLevel 69In the visual model of a square with side (a-b), which areas are added to complete the (a^2) square?EasyLevel 69If the side of a square model is (2x+1), what is the expansion of its area?EasyLevel 69When (a^2-b^2) is changed into a rectangle in an area diagram, what are the sides of the rectangle?EasyLevel 69Which expansion is given by the area model of a square with side (k-4)?EasyLevel 69A square model shows three types of parts (a^2), (2ab), and (b^2). This is the visual proof of which identity?EasyLevel 69How many (x)-rectangle tiles appear in a square with side (x+1)?EasyLevel 69In a rectangle model for ((x+4)(x+1)), what is the sum of the (x)-terms after splitting into four parts?EasyLevel 69Which algebraic identity is represented by a visual model that divides a large square into four parts with areas \(a^2\), \(ab\), \(ab\), and \(b^2\), respectively?EasyLevel 69If a smaller square of side \(b\) is removed from a larger square of side \(a\), which algebraic expression is represented by the remaining L-shaped visual model?EasyLevel 69