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 the square model of (a+b+c), what is the total area of the mixed rectangles?MediumLevel 69In an algebra-tile model, if both sides of a square are \(x+y\), which set of tiles is needed to represent its area?MediumLevel 69A signed rectangle model is formed by (x+3) and (x-5). What will be the total area?MediumLevel 69If a signed rectangle of (x-2) and (x-9) is made, what will be the constant corner?MediumLevel 69Which area tiles are present in the visual model of a square with side \(a+b\)?MediumLevel 69Which identity is represented by an area model in which a square of side \(a+b\) is divided into strips of lengths \(a\) and \(b\)?MediumLevel 69What is the difference between the area models of squares (x+5) and (x+1)?MediumLevel 69In a square model of (x+3), there are (x^2) and two (3x) strips. If the corner is not added, what will be the area?MediumLevel 69If (x^2+10x) is to be shown by completing a square visually, which corner must be added?MediumLevel 69In a visual model, (x^2-6x) must be completed into a square. Which corner should be added to get a perfect square?MediumLevel 69In an area diagram, a square of side (a+1) is divided into four parts. What will be the total area?EasyLevel 73A tile model has (x^2), two (3x) rectangles, and a small square (9). What is the side of the complete square?EasyLevel 73What area is shown by the visual model of a rectangle with sides (p+4) and (p-4)?EasyLevel 73If the outer side in a square model is (y+6), what will be the small corner?EasyLevel 73In a square of side (m+2), what will be the total area of the two equal rectangles?EasyLevel 73A diagram shows a big square (b^2) and a small square (c^2) removed from it. The remaining area equals a rectangle made by which sides?EasyLevel 73If (x^2+4x+4) is made using square tiles, what will be the outer side?EasyLevel 73In the rectangle model of ((r+3)(r+5)), what will be the sum of the (r)-terms?EasyLevel 73In the model of a square with side (n-5), what will be the last term?EasyLevel 73A square model has parts \(u^2\), (10u), and (25). It is the square of which side?EasyLevel 73