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 square model shows four parts (4x^2), (6xy), (6xy), and (9y^2). What will be the outer side?HardLevel 68In a visual model, two strips (ab) and (ab) are removed from an (a^2) square but the corner (b^2) is removed twice. What is the correct remaining area?HardLevel 68If the cut model of (x^2-b^2) is rearranged into a rectangle and one side is (x-b), what is the other side?HardLevel 68A rectangle model has sides (2m+5) and (2m-5). What is the correct simplified area?HardLevel 68A tile model (p^2+18p+81) forms a perfect square. If the middle part is made of two equal rectangles, what is the area of each rectangle?HardLevel 68The outer side of a square is (3a-2b). Based on the visual model, what will be the middle term?HardLevel 68A rectangle for ((x+4)(x+7)) is divided into four parts. Which part is the area of the small corner rectangle?HardLevel 68In a square tile model, one \(x^2\) tile, two \(xy\) rectangular tiles, and one \(y^2\) tile together represent which algebraic identity?HardLevel 68In a model, (a^2-b^2) is cut and rearranged into a rectangle. If the rectangle length is (15) and breadth is (7), which pair for (a) and (b) can be correct?HardLevel 68In a square of side (2x+3), what is the combined area of the two (x)-rectangles?HardLevel 68In a visual model, two strips of width \(b\) are removed from a square of side \(a\). When the common \(b\times b\) corner is added back once, which identity is represented, where \(a>b\)?HardLevel 68If a square model has corner squares (9x^2) and (16) and the middle term is negative, what is the correct area?HardLevel 68A rectangle model has area (x^2+9x+20) and the small corner area is (20). Which sides are possible?HardLevel 68In a square of side (5p-q), what is the combined middle area containing (pq)?HardLevel 68If in a ((a+b)^2) model, the sum of (a^2+b^2) parts is (85) and the sum of two rectangles is (84), what is the area of the whole square?HardLevel 68In a visual model of the algebraic identity \((a+b)^2=a^2+2ab+b^2\), how is the \(2ab\) part usually represented?HardLevel 68The area of a square model is (16a^2+40ab+25b^2). What will be the outer side?HardLevel 68A rectangle model represents ((3x+2)(x+5)). What is the combined sum of the (x)-terms in the four parts?HardLevel 68If a visual model of ((2x-3)^2) is made, which area expression gives the correct final form after subtraction and addition?HardLevel 68In a cut-and-paste model, the area of (a^2-b^2) is (96) and (a-b=6). What is (a+b)?HardLevel 68