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 the tile model of (3x^2+10x+3) forms a factor rectangle, which sides are correct?ExpertLevel 67In a visual model, ( (x+2)^2 ) is subtracted from ( (x+6)^2 ). What is the remaining area equal to?ExpertLevel 67If the outer square has side (x+5) and the inner square has side (x-1), what is the border area?ExpertLevel 67A square of (a+b) is cut into four parts and changed into a rectangle. If one side of the rectangle remains (a+b), what will the other side be?ExpertLevel 67In a square model of (x+3), (x^2) and (9) are colored separately. If the uncolored area is (30), what is the value of (x)?ExpertLevel 67If in a square model of (x-4), the added-back corner is (16) and final area is (81), what is the positive value of (x)?ExpertLevel 67In a rectangle model, (x+2) and (x+5) are replaced by (x+3) and (x+4). What is the difference between the two areas?ExpertLevel 67In a visual proof, ( (a+b)(c+d) ) is divided into four small rectangles. Which decomposition is correct?ExpertLevel 67If area models of ( (x+2)(x+8) ) and ( (x+5)^2 ) are compared, which is larger and by how much?ExpertLevel 67A grid model has total area (x^2+2kx+k^2). When will it be a visual model of a perfect square?ExpertLevel 67If (x^2-2kx+k^2) is made by a subtraction square model, what will be the side?ExpertLevel 67In a square model of (x+y), if two (xy) rectangles are combined into one long rectangle, what is its area?ExpertLevel 67If the model of ( (a+b+c)^2 ) shows (a^2+b^2+c^2) and (2ab+2bc), which part is missing?ExpertLevel 67In a model, the (16) corner is removed from ( (x+4)^2 ) but the strips are kept. What is the remaining area?ExpertLevel 67If in the visual model of ( (2x+7)^2 ), (4x^2) and (49) are already present, what is the missing strip area?ExpertLevel 67A rectangle model forms signed tiles for ( (x-5)(x-7) ). What is the visual meaning of the middle term?ExpertLevel 67If tiles of (x^2-12x+35) form a rectangle, which sides make the model correct?ExpertLevel 67In a square model of (a-b), after removing two (ab) strips from (a^2), what error may occur?ExpertLevel 67If two squares have sides (x+k) and (x-k), what will the difference of their area models be?ExpertLevel 67A visual model compares the area of ( (x+a)(x+b) ) and ( (x+\frac{a+b}{2})^2 ). How much greater is the second area than the first?ExpertLevel 67