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
Two strips of areas (4x) and (4x) are removed from a large square and a corner of area (16) is added back. If the original square was (x^2), the resulting area equals what?ExpertLevel 68In a square of side (u+v), the areas (u^2+v^2) are shown in a different color. What term is obtained by adding the areas of the remaining two equal rectangles?ExpertLevel 68In a rectangle model, the length is (2x+3) and the width is (2x-3). Which area identity does it show?ExpertLevel 68In a square tile model, the central square is (9a^2), the combined area of two equal strips is (30ab), and the small square is (25b^2). What is the side of the whole square?ExpertLevel 68In a model, strips of total area (14x) are added on two sides of an (x^2) square. How much corner area must be added to complete the square?ExpertLevel 68Which visual arrangement best forms the square model for (y^2-6y+9)?ExpertLevel 68In a rectangle model, (x^2+13x+36) must be split into two linear parts. Which pair is correct?ExpertLevel 68If the region (a^2-b^2) in a tile model is rearranged into a rectangle and its length becomes (a+b), what is its width?ExpertLevel 68A model shows the difference between the areas of ((a+b)^2) and ((a-b)^2). What will this difference equal?ExpertLevel 68A square model is to show ((2x+5)^2). What will be the areas of the four parts?ExpertLevel 68In a visual model of an algebraic identity, a large square is divided into one small square, two congruent rectangles, and another small square. Which identity does it represent?ExpertLevel 68In a square of side (a+b), two perpendicular cuts, not a diagonal, divide the side into parts (a) and (b). What is the correct visual sum of areas?ExpertLevel 68In the model of (x^2+2xy+y^2), if (y) is drawn very small, which conclusion still remains correct?ExpertLevel 68A rectangle is divided into parts (x^2), (5x), (7x), and (35). What are the possible sides of the rectangle?ExpertLevel 68A square model has area (16p^2-40pq+25q^2). It represents a square with which side?ExpertLevel 68A visual model compares (a^2+2ab+b^2) with (a^2+b^2). Which area belongs only to the cross rectangles?ExpertLevel 68If the tile model of (x^2+9x+20) forms a complete rectangle, which arrangement is correct?ExpertLevel 68In a square model for ((3x-2y)^2), what will be the combined area of the two removed strips?ExpertLevel 68Which model gives the most direct visual explanation of ((a+b)(a-b)=a^2-b^2)?ExpertLevel 68In a model, (x^2+2xk+k^2) is a perfect square. If the total area of the linear strips is (16x), what is the corner area?ExpertLevel 68