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 visual area model for \((a-b)^2\) is made by removing two strips of width \(b\) from a square of side \(a\). Why is \(b^2\) added in this model?MediumLevel 65From a large square (a^2), two strips (ab) are removed and the small corner square (b^2) is added back. The remaining area equals what?MediumLevel 65A rectangle has length (a+b) and breadth (a-b). Which identity does its tile model show?MediumLevel 65A square with side (x+4) is divided into (x^2), (4x), (4x), and (16) parts. What is the total area?MediumLevel 65A square has side (p+6). In the visual model what area will the small corner square show?MediumLevel 65The model has a (y^2) square and two equal (5y) strips. The small corner is (25). It is the square of what?MediumLevel 65If ((m-3)^2) is shown by an area model, what will be the total area of the middle parts?MediumLevel 65Two strips of width (7) are added along two sides of an (x) by (x) square and a (7) by (7) corner square is added. What is the new area?MediumLevel 65Which visual partition is correct for ((r+2)^2)?MediumLevel 65A rectangle is divided into (x^2), (3x), (5x), and (15) parts. What are the possible sides of the rectangle?MediumLevel 65A tile model forms (x^2+9x+20) as a rectangle. Which sides will be correct?MediumLevel 65In which area model is (a^2-16) directly visible?MediumLevel 65A (10) by (10) square is reduced by removing strips of width (2) to show an (8) by (8) square. Which numerical identity does it explain?MediumLevel 65Which model can be used to find (99^2) easily?MediumLevel 65A square has side (2x+3). What will be the total area of the middle parts in the area model?MediumLevel 65In the model of a square with side (3y+2), which is the largest square-type part algebraically?MediumLevel 65In a visual model (4x^2), (12x), and (9) make a perfect square. What is the side of that square?MediumLevel 65Which tile group represents ((2a-5)^2)?MediumLevel 65A rectangle has sides (x+2) and (x+7). What will be the middle term in the area model?MediumLevel 65A rectangle has an (x^2) square, (6x) and (4x) strips, and a (24) corner. What are its sides?MediumLevel 65