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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

In a square model, the side is (x+1). What will its area be equal to?EasyLevel 71In a square with side (a+2), what is the area of the small corner square?EasyLevel 71If a rectangle has length (x+3) and breadth (x+1), what is the total area from the area model?EasyLevel 71In the area model of a square with side a+b, which area appears as two congruent rectangles?EasyLevel 71When a square of side (m+n) is divided into four parts, which term appears twice?EasyLevel 71If the side of a big square is (p+5), what will be the whole area?EasyLevel 71A square has side (a-b). How will its area be written?EasyLevel 71Which algebraic expression can be represented by a square divided into two squares of areas \(a^2\) and \(b^2\), and two rectangles of area \(ab\) each?EasyLevel 71If an area model of (a^2-b^2) is to be made, which part is removed?EasyLevel 71The area of a rectangle with length (r+s) and breadth (r-s) is equal to what?EasyLevel 71If (11^2) is seen using the area model of ((10+1)^2), what is the total area of the two rectangles?EasyLevel 71The area model of a square with side (20-1) shows the square of which number?EasyLevel 71Which is the correct classification of area parts in the square visual model of \((a+b)^2\)?EasyLevel 71In an area model of a square with side a+b, which parts represent a^2+2ab+b^2?EasyLevel 71In the rectangle model of ((x+2)(x+4)), what is the area of the constant part?EasyLevel 71In a visual model using algebra tiles, the expression \(x^2+2xy+y^2\) represents the area of which figure?EasyLevel 71In the square model of \((2x+1)^2\), what will be the area of the larger square?EasyLevel 71An area model shows regions with areas \(a^2\), \(b^2\), and two rectangular regions each of area \(ab\). Which algebraic expression does this model represent?EasyLevel 71In which visual model is (2ab) shown as two equal rectangles?EasyLevel 71If (15^2) is seen as ((10+5)^2), what is the area of the large square?EasyLevel 71