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 square model of (u+v+w), what will be the total area of the mixed rectangles?ExpertLevel 67If a model has parts (x^2), (8x), (15x) and (120), what are the possible sides of the rectangle?ExpertLevel 67A student wrote the middle term (6x) in the model of ( (2x+3)^2 ). What is the correct visual correction?ExpertLevel 67In a square of side (5t-2), what is the total area of the two subtracted strips?ExpertLevel 67If a square model of (x+12) gives \(x^2\) and a corner (144), which part will complete the model?ExpertLevel 67A rectangle model has (2a+5) and (a-3). Which area is correct after adding the four parts?ExpertLevel 67In an area model, a positive tile (12x) and a negative tile (-5x) are together. What is the combined linear area?ExpertLevel 67If ( (x-4)(x+9) ) is expanded by a signed tile model, what constant corner is obtained?ExpertLevel 67In a square area model, a large square is divided into four parts: one region has area \(x^2\), two equal rectangles each have area \(xy\), and one small square has area \(y^2\). Which algebraic identity does this model represent?ExpertLevel 67If (y^2-14y+49) is shown as a visual square model, what is the area of each removed strip?ExpertLevel 67In a square of side (2m+3n), what will be the combined area of the two mixed rectangles?ExpertLevel 67If a model is made for a square of side (3a-2b), which final expansion is correct?ExpertLevel 67A rectangle model shows (4x^2-25y^2). Which sides can form it?ExpertLevel 67In a visual proof, ( (a+b)^2-(a-b)^2 ) is rearranged into four equal rectangles. What is the area of each rectangle?ExpertLevel 67If the sum of only the squares is removed from the area model of ( (x+y+z)^2 ), what remains?ExpertLevel 67In a square model of side a + b, if a² + b² is placed near the diagonal, what is the total area of the remaining two parts?MediumLevel 67If the area difference between the models of ( (a+b)^2 ) and (a^2+b^2) is asked, what is the correct difference?ExpertLevel 67A model shows the difference of two squares ( (2x+1)^2-(2x-1)^2 ). What is the result?ExpertLevel 67In signed rectangle tiles for (x+4) and (x-2), what will be the total area of the (x)-tiles?ExpertLevel 67A model converts (2x^2+7x+3) into a rectangle. Which split gives the correct visual construction?ExpertLevel 67