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
If the side of a square is divided into two parts, \(x\) and \(y\), which algebraic identity is represented by the visual model of the whole square's area?EasyLevel 71Which set of regions is shown in an area model for the identity \((a+b)^2\)?EasyLevel 71Why is the final (b^2) part added in a square with side (a-b)?EasyLevel 71If \(x^2\) and (4) are shown in the \((x+2)^2\) model, what is the total area of the two middle rectangles?EasyLevel 71In a grid, (x) and (3) are written on the top, and (x) and (2) on the side. What will be the total area?EasyLevel 71Which area model shows (x^2-9)?EasyLevel 71If ((a+4)(a-4)) is seen through a rectangle area model, what will be the result?EasyLevel 71In the area model of a square with side (3+2), what will be the total area of the two rectangles?EasyLevel 71If (7^2) is shown as ((5+2)^2), the whole area will be formed by the sum of how many parts?EasyLevel 71In an area model representing the square of
a-b
, which type of region is subtracted twice?EasyLevel 71What is the total area in the visual model of a square with side (x+4)?EasyLevel 72If a square model has (x^2), two (6x) rectangles, and a small square (36), what is the outer side?EasyLevel 72In a square with side (a+5), what will be the total area of the two equal rectangles?EasyLevel 72What is the sum of the four parts in the rectangle model of ((x+2)(x+5))?EasyLevel 72Which expansion is correct in the area model of a square with side (y-3)?EasyLevel 72A large square has side (m), and the removed small square has side (n). The remaining area is linked to which identity?EasyLevel 72In the visual model of the algebraic identity \((a+b)^2=a^2+2ab+b^2\), what kind of regions does the term \(2ab\) represent?EasyLevel 72If the total area of a square model is (x^2+2x+1), what will be its side?EasyLevel 72Which expansion is given by the area model of a rectangle with dimensions (a+3) and (a+7)?EasyLevel 72Using the visual identity, what is the area of a square with side (10+2)?EasyLevel 72