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 of side \(x+7\), the small corner square is \(7^2\). What is its area?EasyLevel 68If a square area model has parts \(x^2\), \(5x\), \(5x\), and \(25\), what is the whole area?EasyLevel 68Which option correctly writes the visual area of \((x+2)^2\)?EasyLevel 68Which option correctly gives the visual area of \((x-4)^2\)?EasyLevel 68If \(52^2\) is solved using the area model of \((50+2)^2\), what is the large part \(50^2\)?EasyLevel 68In the visual model of \(49^2\), using \((50-1)^2\), which is the small square?EasyLevel 68In an area model, what expansion is obtained by adding the parts of \((x+3)(x+3)\)?EasyLevel 68In which model is an identity explained by only adding areas?EasyLevel 68What is the main visual difference between \((a+b)^2\) and \((a-b)^2\) in square models?EasyLevel 68If a visual model has total area \(p^2+2pq+q^2\), what is the side of the whole square?EasyLevel 68Which algebraic identity is shown by the area model of a square with side \(a+b\)?EasyLevel 70By observing a square of side \(x+3\), what is the expansion of \((x+3)^2\)?EasyLevel 70A large square has side \(a\), and a square of side \(b\) is removed from it. How is the remaining area expressed?EasyLevel 70The area of a rectangle with dimensions \(a+b\) and \(a-b\) is linked with which identity?EasyLevel 70Which expansion is correctly shown by the area model of a square with side \(x-2\)?EasyLevel 70If a square is divided into parts \(p^2\), \(pq\), \(pq\), and \(q^2\), what is its total area?EasyLevel 70In a square of side \(m+n\), which can be the largest square part among its four parts?EasyLevel 70An \(x\) by \(x\) square, two \(x\) by \(5\) rectangles, and one \(5\) by \(5\) square are combined. This is a model of what?EasyLevel 70If a visual model subtracts two \(4y\) rectangles from a \(y^2\) square and adds a \(16\) square, what is the identity?EasyLevel 70In the area model of a square with side \(6+2\), how can the total area be written?EasyLevel 70