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
Which model can give the value of ((50+2)^2) without long multiplication?MediumLevel 65In a rectangle model, the top labels are (x) and (4), and the left labels are (x) and (-6). What is the total area?MediumLevel 65In which visual proof is (a^2+2ab+b^2) seen as one large square?MediumLevel 65A student confused the model of (a^2-b^2) with ((a-b)^2). Which area should have been extra in his answer?MediumLevel 65If the model of (x^2+6x+9) is a perfect square, what is the area of each of the two equal rectangular strips?MediumLevel 65A rectangle area model shows (2x^2+7x+3). If the sides are (2x+1) and (x+3), what will the areas of the small rectangles be?MediumLevel 65A square has side \(a+b\). It is divided into four regions with areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Which algebraic identity does this visual model represent?MediumLevel 65Visually, what is the difference between the areas of squares with sides (x+2) and (x+4)?MediumLevel 65In the visual model of (x^2+2xy+y^2), what whole shape is formed?MediumLevel 65If a square model has main square (16p^2), two strips (20p) and (20p), and corner (25), what is the outer side?MediumLevel 65Assume that \(a>b\). In the area model of \(a^2-b^2=(a+b)(a-b)\), after removing the smaller square from the larger square and rearranging the remaining pieces, which rectangle is formed?MediumLevel 66Why do two rectangles of area \(ab\) appear in the visual model of a square with side \(a+b\)?MediumLevel 66A rectangle has length (a+b) and breadth (a-b). What result is shown by the area model?MediumLevel 66In a square visual model, each side of the large square is divided into two parts, \(a\) and \(b\). The model forms four regions with areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Which algebraic identity does it represent?MediumLevel 66A visual model shows a square of side (p+3). Which expansion is formed by its corner square and strips?MediumLevel 66In a square of side (y+5), the middle square is (y^2). Choose the identity using the two equal strips and corner.MediumLevel 66A square has side (m-2). Which parts must be subtracted and added from the (m^2) model to get the correct area?MediumLevel 66If a visual model is made for a square of side (z-7), what will be the expansion?MediumLevel 66A rectangle has length (r+6) and breadth (r+2). Which expansion is obtained from the area model?MediumLevel 66In an area model, a rectangle is formed by (s+3) and (s+8). From what is the constant part formed?MediumLevel 66