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 rectangle model (x^2+2x-15) must be shown using two binomial sides. Which sides are correct?MediumLevel 67A visual model of a square with side 2a + 5 will show which area parts?MediumLevel 67What is the middle term in the visual expansion of a square with side (5x-1)?MediumLevel 67Each side of a square is divided into two parts, \(a\) and \(b\). The model shows regions of areas \(a^2\), \(b^2\), and two rectangles each of area \(ab\). Which algebraic identity does this model represent?MediumLevel 67A rectangle has sides (a+b) and (a+b). How many (ab) rectangles appear in the area model?MediumLevel 67Which visual model can directly explain (x^2-16)?MediumLevel 67A rectangle with sides (m+2) and (m+8) shows which expression in an area model?MediumLevel 67If a square of side (a-b) has final area (a^2-2ab+b^2) then why does the (+b^2) part appear?MediumLevel 67Square tiles form (x^2+14x+49). Which two equal strip areas must have been added?MediumLevel 67A visual model has area (x^2-6x+9). It is the area of a square with which side?MediumLevel 67A rectangle has sides (2x+1) and (2x-1). What area is obtained from the visual model?MediumLevel 67In the area model of \((p+q)^2\), which two parts are always rectangles of equal area?MediumLevel 67A rectangle model must show (x^2-9x+20) in factors. Which pair is correct?MediumLevel 67What is the middle term in the visual expansion of a square with side (a+2b)?MediumLevel 67A square model shows (16p^2-24p+9). It is equal to which square?MediumLevel 67If a rectangle is made with sides (3x+2) and (3x-2) then which area is obtained?MediumLevel 67Which algebraic expression is best represented by an area model that divides a large square into four parts—two squares of different sizes and two congruent rectangles?MediumLevel 67In a rectangle model with sides (x-2) and (x+6) what will be the constant part?MediumLevel 67In which visual identity do two equal rectangles give middle term (18x) and the small square is (81)?MediumLevel 67In a square model the large square is (a^2) and the removed small square has area (b^2). If the remaining part is made into a rectangle then how is the area written?MediumLevel 67