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 the rectangle model of (x^2+11x+30), the small corner area is (30). Which strips are correct?MediumLevel 65If (a^2-b^2) is to be shown visually, which idea is most suitable?MediumLevel 65A square with which side will give the area model (x^2+18x+81)?MediumLevel 65In a square visual model, the areas of two smaller squares are \(a^2\) and \(b^2\), and each of the remaining two rectangles has area \(ab\). Which algebraic identity does this model represent?MediumLevel 65When a rectangle with sides (a+3) and (a-3) is rearranged, what area is obtained?MediumLevel 65Which visual model explains (25x^2-36)?MediumLevel 65What is the difference between the areas of squares with sides (x+1) and (x-1)?MediumLevel 65Which set of four regions is correct in the area model of a square with side (x+10)?MediumLevel 65In a rectangle model, the vertical parts are (x) and (8), and the horizontal parts are (x) and (2). What is the total area?MediumLevel 65If the tile model of (x^2+13x+36) has corner (36), which constant sides are correct?MediumLevel 65Which model can change (x^2-25) into a rectangle with sides (x+5) and (x-5)?MediumLevel 65A visual model shows (9a^2+24a+16) as a perfect square. What will its side be?MediumLevel 65What is the middle term in the visual model of a square with side (4x-1)?MediumLevel 65A tile model has parts (x^2), (-3x), (-7x), and (21). Which product does it represent?MediumLevel 65In a visual model, strips (4x) and (9x) are removed from an (x^2) square and a (36) corner is added. Which rectangle is formed?MediumLevel 65Which area model helps factorize (x^2-2x-15)?MediumLevel 65What is the visual result of subtracting the area of a square with side (x-6) from a square with side (x+6)?MediumLevel 65In which situation will a visual model definitely have two equal rectangular strips?MediumLevel 65A student wrote only (x^2+25) in the model of ((x+5)^2). Which part was missed?MediumLevel 65Why is the small (8) by (8) square added while making the area model of a square with side (x-8)?MediumLevel 65