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 visual model is correct for (9r^2-16)?MediumLevel 68In a rectangle with sides (x+1) and (x+9), what will be the sum of middle strips?MediumLevel 68A visual model is made by dividing each side of a square into two parts, \(a\) and \(b\). Which algebraic identity represents the total area of this model?MediumLevel 68When (b^2) is removed from a large square, the remaining area is (a^2-b^2). Which product represents it?MediumLevel 68If a square of side \(a+b\) is divided into four parts of sizes \(a\times a\), \(a\times b\), \(b\times a\), and \(b\times b\), which algebraic identity does it visually represent?MediumLevel 68A square area model is divided into four parts with areas \(x^2\), \(xy\), \(xy\), and \(y^2\). Which algebraic identity does this model represent?MediumLevel 68Which area partition correctly represents the visual model of a square with side
a+b
?MediumLevel 68What is the expansion of the area model of a square with side (2u-1)?MediumLevel 68Which two strips will be in the rectangle model (x^2+5x+6)?MediumLevel 68In which visual model do (a^2+2ab+b^2) and ((a+b)^2) show the same area?MediumLevel 68Which expansion is correct in the model of a square with side (x-7)?MediumLevel 68An (x + 4) by (x + 6) rectangle is compared with an (x + 5) by (x + 5) square. Which area is larger?MediumLevel 68If (x^2+16x+64) is a square model, what is the outer side?MediumLevel 68Which algebraic expression is represented by a visual model in which one large square is divided into four parts—one square, two equal rectangles, and one smaller square?MediumLevel 68A rectangle model has sides (2x+3) and (x+4). What will be the total area?MediumLevel 68In a square with side (3x-2), what will be the small corner and the middle area?MediumLevel 68Which visual model can give the factorization of (x^2+18x+80)?MediumLevel 68If the models of ((x+2)^2) and ((x+2)(x-2)) are compared, how much greater is the first area than the second?MediumLevel 68A square model has (x^2), (kx), (kx), and (36). If the perfect square side is (x+6), what is (k)?MediumLevel 68In a square with side (a+2b), what will be the total rectangular area involving (b)?MediumLevel 68