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 square model, the outer area is ((x+y)^2) and the sum of two small squares is (x^2+y^2). What is the combined area of the two rectangles?HardLevel 68If the tile model (x^2+10x+c) forms a square with side (x+5), what is (c)?HardLevel 68Which visual partition explains the (2ab+2bc+2ca) part of ((a+b+c)^2)?HardLevel 68A rectangle model represents ((2x+1)(2x+7)). What will be the constant corner and combined (x)-term in the total area?HardLevel 68If the area of a square model is (25x^2-30xy+9y^2), what is its side?HardLevel 68In a visual model, the total area (a^2+2ab+b^2) is (144). If (a+b) is positive, what is the outer side?HardLevel 68If (a+b=13) and (a-b=5), what is the area of the rectangle model of (a^2-b^2)?HardLevel 68A square visual model is divided into four regions: one square of area \(a^2\), another square of area \(b^2\), and two congruent rectangles each of area \(ab\). Which algebraic identity does this model represent?HardLevel 68In a tile model for ((x-4)^2), which areas are subtracted from the (x^2) square and which area is added back?HardLevel 68In a rectangular area model, the length is \(x+y\) and the breadth is \(x-y\), where \(x>y\). Which algebraic identity does this model represent?HardLevel 68If a square model has (a^2+2ab+b^2) but a student wrote only (a^2+b^2), which visual part was missed?HardLevel 68An area model shows ((4x+3y)(4x-3y)). Which area is correct?HardLevel 68If in the square model of ((x+a)^2), each rectangle has area (11x), what will the final small square be?HardLevel 68In the square model of side (x+2y+3z), what is the combined area of the rectangles containing (yz)?HardLevel 68The area of a square model is (x^2+14x+49). If the outer side is (x+k), what is (k)?HardLevel 68A square has side \(p+q\). It is divided into one square of area \(p^2\), one square of area \(q^2\), and two equal rectangles of area \(pq\) each. Which identity does this visual model represent?HardLevel 68Which visual model can catch the mistake that ((x+5)^2) is not (x^2+25)?HardLevel 68In a square visual model, each side is divided into two parts, \(p\) and \(q\). The four regions have areas \(p^2\), \(pq\), \(pq\), and \(q^2\). Which algebraic identity does this model represent?HardLevel 68If the areas of squares with sides (a+b) and (a-b) are subtracted, which area is obtained visually?HardLevel 68A square visual model is divided into one large square, one small square, and two rectangles of equal area. If the areas of these parts are \(a^2\), \(b^2\), and \(ab,ab\) respectively, which algebraic identity does the model represent?HardLevel 68