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 cut-square model, a corner square of side (b) is removed from a square of side (a), and the remaining part is rearranged into a rectangle. What will be the new rectangle sides?ExpertLevel 66In a tile model, (4x^2), (-12xy), and (9y^2) make a perfect square. What will be the outer side?ExpertLevel 66If the rectangle model of (x^2+px+36) is formed by sides (x+4) and (x+9), what is the value of (p)?ExpertLevel 66In the visual model of a square with side (3a+2b), what will be the combined area of the two equal rectangles?ExpertLevel 66A model changes (9m^2-25n^2) into two rectangular side factors. Which sides are correct?ExpertLevel 66A square model (x^2-10x+q) shows a perfect square. If each removed strip has area (5x), what is (q)?ExpertLevel 66Which visual model most directly explains the area of ((2x+7)(2x-7))?ExpertLevel 66In a square tile model, one \(x^2\) square, two \(xy\) rectangles, and one \(y^2\) square combine to form a larger square. Which algebraic identity does this model represent?ExpertLevel 66When a square of side (a+b+c) is partitioned in a visual model, which area expansion is correct?ExpertLevel 66An (x+3) by (x+5) rectangle is compared with an (x+4) by (x+4) square. What is rectangle area minus square area?ExpertLevel 66In a cut-and-paste model, (x^2-14x+49) is changed into a smaller square. What is the side of the new square?ExpertLevel 66Which visual partition is suitable for changing (x^2+xy-20y^2) into a rectangle?ExpertLevel 66In the model of a square with side (5p-2q), what will be the corner term and the middle area respectively?ExpertLevel 66A rectangle model has four cells (8x^2), (12x), (10x), and (15). Which sides are possible?ExpertLevel 66In the visual model of the identity (a+b)², how is the larger square divided?ExpertLevel 66In which visual model can (x^2+2xy+y^2-z^2) be read first as a square and then as a difference of squares?ExpertLevel 66A square model has outer side (2x+3y+z). What is the total area of only the two rectangle pairs involving (z) with (2x) and (3y)?ExpertLevel 66In the area model of a square with side (x+k), the middle term is (18x) and the corner is (81). What is (k)?ExpertLevel 66A subtraction model shows (16x^2-40xy+25y^2). It is the area of a square with which side?ExpertLevel 66Which grid model can factorize (3x^2-11x-20)?ExpertLevel 66