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
Why are (a^2+2ab+b^2) and ((a+b)^2) equal in an area model?EasyLevel 69A rectangle model shows ((x+2)(x-2)). What is its simplified area?EasyLevel 69In a square of side (2a+b), how is the (b^2) part formed?EasyLevel 69If the sides of a rectangle are (a+b) and (c), what two parts appear in the area model?EasyLevel 69A square model shows (x^2-6x+9). It is the area of a square with which side?EasyLevel 69If a square of side \(p+q\) is divided into regions of areas \(p^2\), \(q^2\), and two regions of area \(pq\), which algebraic identity does this visual model represent?EasyLevel 69If the side of the big square is (10) and the side of the small square is (4), what is the area of the difference of squares?EasyLevel 69In a square model, the outer side is (x+8). What will be the last term in the expansion of the area?EasyLevel 69In the visual model of ((a+b)^2), where does the (2ab) part come from?EasyLevel 69A rectangle with sides (x+3) and (x-3) shows which identity?EasyLevel 69A square is divided into two strips with side parts (a) and (b). Which identity is shown by the area of the whole square?MediumLevel 67If a square of side (x+y) has a small corner square of side (y) then what is the total area of the two equal rectangles?MediumLevel 67A small square of side (q) is removed from a large square of side (p). Which is the factor form of the remaining area?MediumLevel 67A rectangle has length (a+b) and breadth (a-b). Its area matches which algebraic identity?MediumLevel 67In a visual model two strips of width (n) are subtracted from a square of side (m) and the corner (n^2) part is added back. Which identity is formed?MediumLevel 67In an area model a square (r^2) is surrounded by two strips of area (rs) and a small square (s^2). What is the total area?MediumLevel 67In a tile model a square of side (u+v) is divided into a square (u^2) a square (v^2) and two rectangles. What is the area of each rectangle?MediumLevel 67If the visual model of a square of side (c-d) is made by removing two (cd) strips from (c^2) then what final correction is needed?MediumLevel 67A square model shows total area (x^2+6x+9). What will be the side of the square?MediumLevel 67A visual model shows area (y^2-8y+16). It is formed from which square side?MediumLevel 67