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
A diagram shows \(12^2-2\times12\times2+2^2\). It is the area of which square?EasyLevel 70If \(9^2-4^2\) is solved using a visual model, which rectangle is formed?EasyLevel 70In a rectangle model, \(x(x+6)\) is shown by which sum?EasyLevel 70How many rectangular \(ab\) parts are there in a square of side \(a+b\)?EasyLevel 70If \(x^2+2xy+y^2\) is made with tiles, what will be the outer side?EasyLevel 70A square model has \(x^2\), two \(2x\) rectangles, and \(4\) unit squares. Which identity is it?EasyLevel 70Which statement is correct for an area model?EasyLevel 70In the visual model of \((m+4)^2\), what is the area of the small square?EasyLevel 70In the rectangle model of \((a+2)(a+5)\), what will be the area of the constant corner?EasyLevel 70In the visual model of \((x+1)(x+4)\), how is the middle \(x\) term formed?EasyLevel 70Which expression can be shown by the area of a square with side \(u-v\)?EasyLevel 70If \(15^2-5^2\) is changed into a rectangle, what will be the area?EasyLevel 70Which small square should be added in the area model of \(x^2+8x\) to make a complete square?EasyLevel 70Which model explains the formation of \(2ab\), \(2bc\), and \(2ca\) in \((a+b+c)^2\)?EasyLevel 70Using identity, what is the area of a square with side \(20-1\)?EasyLevel 70In which situation will the term \(2ab\) not appear in the area model?EasyLevel 70In a square of side \(x+6\), what will be the total area of the two equal rectangles?EasyLevel 70If the total area of a square model is \(x^2+14x+49\), what will be its side?EasyLevel 70In which visual model do the parts combine to form a larger square with side \(a+b\)?EasyLevel 70What is the main benefit of learning identities through an area model?EasyLevel 70