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
When a square of side (a+b+c) is divided into (3) parts in both directions, how many small regions are formed?EasyLevel 71In the grid model of ((a+b+c)^2), what type of parts are (a^2), (b^2), and (c^2)?EasyLevel 71If (ab) is one rectangle in the (a+b+c) model, what area will (ba) give?EasyLevel 71In the area model of a rectangle, the four regions have areas \(x^2\), \(3x\), \(2x\), and \(6\). Which two expressions represent the sides of the rectangle?EasyLevel 71If (18^2) is found using ((20-2)^2), what is the small square added at the end?EasyLevel 71In a rectangle model, length is (x+5) and breadth is (x+2). What will be the total of the (x)-terms?EasyLevel 71Which area model represents the identity
\((a+b)^2=a^2+2ab+b^2\)?EasyLevel 71If \(x^2+12x+36\) is a perfect square area model, what is the whole side?EasyLevel 71In an area-based visual model of a square, which regions are needed to represent \((a+b)^2\)?EasyLevel 71If in a square of side (x+7), the total area of two equal rectangles is (14x), what is the side of the small square?EasyLevel 71In which model is (a^2-b^2) shown as ((a-b)(a+b))?EasyLevel 71If \(24\cdot26\) is viewed as ((25-1)(25+1)), what result will be obtained?EasyLevel 71In the area model of a square with side (2a+3), what is the total area of the two rectangles?EasyLevel 71If ((2x+3)^2) is expanded, which area is correct?EasyLevel 71In a square area model, there are regions of areas a^2, b^2, and two congruent rectangular regions each of area ab. Which algebraic identity does this model represent?EasyLevel 71If the rectangle sides are (3x+1) and (x+2), what will be the total (x)-term in the area model?EasyLevel 71What is the constant part in the area model of ((a+1)(a+6))?EasyLevel 71In a visual model, (x^2+5x+6) can be formed by which rectangle?EasyLevel 71If the side of a big square is (30+2), the whole area is equal to which number?EasyLevel 71A side of a square is divided into two parts, \(a\) and \(b\). The model shows regions of areas \(a^2\), \(b^2\), and two rectangles each of area \(ab\). Which algebraic identity does this model represent?EasyLevel 71