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 area model of \((3x+2)^2\) is drawn, what will be the total area of the (x)-term parts?HardLevel 66A model arranges (25x^2-30x+9) as a square. Which is the correct side?HardLevel 66In the (3)-part grid of a square with side (a+b+c), how many rectangular cross regions are there in total?HardLevel 66Which expansion shows the full area of a square with side (a+b+c)?HardLevel 66In a visual model of \(x^2-y^2\), a smaller square of area \(y^2\) is removed from a larger square of area \(x^2\), and the remaining parts are rearranged. What are the sides of the rectangle formed?HardLevel 66In a rectangle model, which option correctly writes (x^2-13x+40) as two sides?HardLevel 66A square area model has side \(p+q\). It is divided into one square of area \(p^2\), one square of area \(q^2\), and two rectangles each of area \(pq\). Which algebraic identity does this model represent?HardLevel 66A square of side (5) is removed from a square of side (12). How will the remaining area be written using the ((a-b)(a+b)) model?HardLevel 66If a square of side
a+b
is divided into four parts, which partition correctly gives a visual representation of
a^2+2ab+b^2
?HardLevel 66An area model shows (16a^2+40ab+25b^2). It is the area of a square with which side?HardLevel 66If a square with side (3x+4) is modeled, what will be the contribution of the constant square to the total area?HardLevel 66In a square of side (x+y), the sum of (x^2) and (y^2) parts is (50) and the total area of two rectangles is (48). What is the area of the whole square?HardLevel 66If in the model of ((x-6)^2), two rectangles are removed from (x^2) and a small square is added back, what is the added-back area?HardLevel 66Which visual model can immediately connect (x^2+2xy+y^2-z^2) with ((x+y-z)(x+y+z))?HardLevel 66If a square of side \(p+q\) is divided according to lengths \(p\) and \(q\), which parts must appear in the visual area model of \((p+q)^2\)?HardLevel 66In an area model of a square with side \(a\), strips of width \(b\) are removed along two adjacent sides. The common \(b\times b\) corner is added once to correct for being removed twice. Which identity does this model represent?HardLevel 66If a rectangle model has total area (2x^2+7x+3), which pair of sides can be correct?HardLevel 66In an area model, two strips of size \(a\times b\) are removed from a square of side \(a\), and their common \(b\times b\) region is added back once. Which algebraic identity does this model represent?HardLevel 66Which arrangement of regions must appear in an area model of the identity \((a+b)^2=a^2+2ab+b^2\)?HardLevel 66Each side of a square is \(a+b\). It is divided into four regions with areas \(a^2\), \(ab\), \(ab\), and \(b^2\). Which algebraic identity does this visual model represent?HardLevel 66