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Subjects

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

Which figure directly shows the area ((u-v)^2)?EasyLevel 72If (x^2+12x+36) is read through a complete square model, what is the side of the small square?EasyLevel 72In the visual model of ((r+s)(r-s)), why do the middle terms not remain?EasyLevel 72What is the area of (x(x+9)) in the rectangle model?EasyLevel 72What is the total area in the visual model of a square with side (2x+1)?EasyLevel 72Which algebraic expression has a visual model of one large square containing a square of area \(x^2\), a square of area \(y^2\), and two equal rectangles of area \(xy\)?EasyLevel 72In the model of a square with side (x-5), what will be the area of the final small square?EasyLevel 72In which visual model are the four area parts of (a^2+2ab+b^2) clearly visible?EasyLevel 72If a rectangle model has parts (x^2), (4x), (5x), and (20), what can the outer dimensions be?EasyLevel 72A student writes ((x+3)^2) as (x^2+9). According to the visual model, what is missing?EasyLevel 72Which identity is proved by equating the area of a square with side (a+b) and the sum of its inner parts?EasyLevel 72Using identity, what is the area of a square with side (8-1)?EasyLevel 72Which visual model shows (a(a+b)) by combining one (a^2) square and one (ab) rectangle?EasyLevel 72If ((x+4)(x-4)) is viewed through a rectangle model, what will the area be?EasyLevel 72In a square with side (3x+2), what will be the area of the small square?EasyLevel 72In a visual model, (x^2-10x+25) shows the side of which square?EasyLevel 72If (6^2-2^2) is changed into a visual rectangle, what will the dimensions be?EasyLevel 72Which partition is correct in the area model of the algebraic identity \((a+b)^2\)?EasyLevel 72In the visual model of a square with side (a+b+c), how many times will the (bc) rectangle appear?EasyLevel 72If (x^2+16x+64) is a complete square model, what is the outer side?EasyLevel 72