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
If a rectangle with sides (a+2) and (a+9) is divided into four parts, what will be the middle term?MediumLevel 66A visual model of a rectangle (n+4) by (n-4) is made. Which parts cancel?MediumLevel 66What will be the final area in the rectangle model of (t+5) and (t-5)?MediumLevel 66In a square area model, each side is divided into two parts, a and b. The areas of the resulting regions are a², ab, ab, and b². Which algebraic identity does this model represent?MediumLevel 66In a square area model, one part has area \(a^2\), two rectangular parts have area \(ab\) each, and one part has area \(b^2\). Which algebraic identity does this model represent?MediumLevel 66If parts are made in a rectangle model of (q+1) and (q+6), what is the simplified total area?MediumLevel 66An area model is made for a square of side (2x+3). Which expansion is correct?MediumLevel 66A square has side (3a+2). In the area model, what will be the total middle strip area?MediumLevel 66In a square of side (2p+5), what will be the area of the small constant corner?MediumLevel 66A model has total area (4r^2), (20r) and (25). It can be formed from a square with which side?MediumLevel 66If the area of a square model is (9x^2+24x+16), what will be its side?MediumLevel 66Which expansion is correct in the visual model of a square with side (5y-1)?MediumLevel 66A large square (25k^2) is shown. Two (15k) strips are subtracted and (9) is added. Which square is formed?MediumLevel 66In a rectangle model, the length is (2a+3) and breadth is (2a-3). What will be the area?MediumLevel 66In the rectangle model formed by (3m+7) and (3m-7), which term will not remain?MediumLevel 66A rectangle has length (x+10) and breadth (x-10). Which constant term is subtracted by the visual model?MediumLevel 66A tile model has area (x^2+9x+20). How can it be shown as sides of a rectangle?MediumLevel 66The area model \(v^2+13v+36\) must be changed into a rectangle. Which sides are correct?MediumLevel 66A model has tiles (x^2+12x+36). Which shape does it most directly show?MediumLevel 66If (a^2-8a+16) is to be shown visually as a square, what will be the side of the square?MediumLevel 66