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 visual model of a square with side \(x-2\), which term remains positive?EasyLevel 68In which visual model do two equal rectangle areas combine to form \(2ab\)?EasyLevel 68In a rectangle model, into how many parts is \((x+1)(x+4)\) most simply divided?EasyLevel 68In the rectangle model of \((x+1)(x+4)\), what is the total of the \(x\)-terms?EasyLevel 68If the area model of a rectangle is \((a+3)(a+2)\), what is the area of the constant part?EasyLevel 68While making the visual model of \((a+b+c)^2\), which term appears twice?EasyLevel 68How many square terms are there in the area model of \((a+b+c)^2\)?EasyLevel 68If a square of side \(a+b+c\) is split into \(3\) parts in each direction, how many small sections are formed?EasyLevel 68Which model shows \(a^2+2ab+b^2\) as a complete square?EasyLevel 68In which model can \(a^2-2ab+b^2\) be seen?EasyLevel 68If \(13^2\) is understood using the visual model of \((10+3)^2\), what is the \(2ab\) part?EasyLevel 68In the visual model of \(15^2\) using \((10+5)^2\), what is the area of the small square?EasyLevel 68If \(18^2\) is seen using the model \((20-2)^2\), which term will be subtracted?EasyLevel 68In an area model, \(x^2+9x+18\) can come from which product?EasyLevel 68What is the relation between the rectangle model \((x+4)(x+4)\) and the square model \((x+4)^2\)?EasyLevel 68Which method is correct to explain \(a^2-b^2\) visually?EasyLevel 68Which identity is modeled by drawing a rectangle with sides \(a+b\) and \(a-b\)?EasyLevel 68In a square model, \(x^2+2xy+y^2\) is the area of a square with which side?EasyLevel 68In a visual model, \(x^2-6x+9\) can be shown by a square of which side?EasyLevel 68If \(21 \times 19\) is seen as \((20+1)(20-1)\), which identity is used?EasyLevel 68