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 an area model, the big square has side (x+5) and two squares of areas (x^2) and (25) are shown. What is the total area of the remaining two equal rectangles?HardLevel 66If in a square of side (a+b), the (a^2) part is (49) and the (b^2) part is (9), what is the area of the whole square?HardLevel 66A square model shows area (x^2+14x+49). What is the side of the small square in this model?HardLevel 66A square of side (q) is removed from a square of side (p), and the remaining part is rearranged into a rectangle. What are the sides of the new rectangle?HardLevel 66To show (x^2-8x+16) as a perfect square in a visual model, a square of which side will be made?HardLevel 66If (38^2) is understood through the visual model of ((40-2)^2), what is the total area of the two rectangles removed?HardLevel 66In a rectangle model, the length is (x+6) and the breadth is (x-2). What is the total area after adding the parts?HardLevel 66Which area model will form four parts (x^2), (7x), (-3x), and (-21)?HardLevel 66A square model has total area (4x^2+12x+9). What is the side of the whole square?HardLevel 66If a visual model shows (9a^2-24ab+16b^2) as a perfect square, which one is it?HardLevel 66In a model, a square of side (a+b+c) is divided into (3) parts in both directions. What is the total area related to (ab)?HardLevel 66In the visual model of ((2x+5)^2), what forms the middle area?HardLevel 66In the area model of the algebraic identity \((a+b)^2=a^2+2ab+b^2\), how is the \(2ab\) part represented?HardLevel 66In an area model, (x^2+6x) has to be made into a perfect square. What is the area of the small empty corner?HardLevel 66If (x^2-10x) is to be made a perfect square using a subtraction square model, which term will be added?HardLevel 66In a square of side (a+b), only the two rectangles are shaded, leaving (a^2) and (b^2) unshaded. What is the shaded area?HardLevel 66Assume that \(x>y\). Which rectangle can directly represent \(x^2-y^2\) as an area?HardLevel 66Which visual arrangement can most directly show ((a+b)^2-(a-b)^2=4ab)?HardLevel 66If \(27 \times 33\) is treated as ((30-3)(30+3)) in a visual model, what is the area?HardLevel 66A rectangle has sides (2x+3) and (2x-3). What area is obtained from the visual model?HardLevel 66