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 visual model, (25x^2-1) is rearranged into a long rectangle. What will be the rectangle sides?ExpertLevel 66If the total area of a square model is (x^2+14xy+49y^2), what is the area of each equal rectangle?ExpertLevel 66The difference between squares of sides (2a+b) and (2a-b) equals which visual area?ExpertLevel 66Which model first changes (x^2-4xy+4y^2-z^2) into a smaller square and then into a difference?ExpertLevel 66In a rectangle model, the small corner area is (-30) and the sum of middle strips is (x). For (x^2+x-30), which sides are correct?ExpertLevel 66Which visual comparison can find (101^2-99^2) immediately?ExpertLevel 66In a square of side (x+2), a square of side (x-2) is placed at a corner. How will the remaining outer area be expressed?ExpertLevel 66A large square model contains (a^2+b^2+c^2+2ab+2ac+2bc). If all strips involving (c) and the (c^2) corner are removed, what area remains?ExpertLevel 66In which rectangle model will the middle areas of (15x^2-2x-8) appear as (10x) and (-12x)?ExpertLevel 66In a visual proof, ( (a+b+c)^2-(a+b-c)^2 ) is read as a difference of two squares. What is the remaining area?ExpertLevel 66In a square of side (a+b), if the widths of the (a) strip and (b) strip are interchanged but the total side remains the same, which area relation remains unchanged?ExpertLevel 67A square model has (x^2), two equal rectangles and a corner (49). If the whole square has side (x+7), what is the combined area of the two rectangles?ExpertLevel 67If rectangles of area (pq) are placed at opposite positions in a square of side (p+q), how many such rectangles will be present?ExpertLevel 67A model shows m² + 18m + 81 as a square. Which expression represents the side of this square?MediumLevel 67In a visual model, the large square is (16y^2) and the small added square is (25). If two strips are subtracted, which area is correct?ExpertLevel 67In a rectangle model, (r+11) and (r-11) are placed together. Which linear parts cancel visually?ExpertLevel 67If in the rectangle model of (3x+4) and (3x-4), the (3x) part is treated as the square side, what area remains?ExpertLevel 67A tile arrangement \(x^2+15x+54\) forms a rectangle. Which constant strips make this arrangement possible?ExpertLevel 67A square model has (25a^2+60a+36). What are the side of the small corner and the side of the large part respectively?ExpertLevel 67If a square of side (a+b+c) is cut into three parts to make a model, how many rectangles of type (ab) will appear?ExpertLevel 67