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 visual area model of a square with side \(a+b\), which of the following statements is correct?MediumLevel 69In a square of side (y+6), the large square is (y^2). What is the combined area of both strips?MediumLevel 69If the corner of a square of side (a+5) is (25), which expansion is complete?MediumLevel 69A square has side (m-3). After removing two strips from the large (m^2) square and adding the corner back, which area is obtained?MediumLevel 69A rectangle has sides (p+4) and (p+7). What simplified form comes from the area model?MediumLevel 69If a rectangle with sides (r+8) and (r-8) is made, what result is obtained?MediumLevel 69A grid has parts (x^2), (9x), (2x), and (18). It can be seen as a rectangle with which sides?MediumLevel 69A visual model is made for a square of side (2x+5). Which expansion is correct?MediumLevel 69In the area model of a square with side
a+b
a+b
, which shapes represent the term
2ab
?MediumLevel 69If a large square is divided into four regions with areas \(x^2\), \(xy\), \(xy\), and \(y^2\), which algebraic identity does this visual model represent?MediumLevel 69An area model has (z^2+16z+64). What is the area of the small corner?MediumLevel 69In a square of side (n-5), what is the total area of the two removed strips?MediumLevel 69If the final area of a square of side (q-4) is needed, which expansion is correct?MediumLevel 69In a rectangle model, the sides are (s+3) and (s-3). Which area is correct?MediumLevel 69Area tiles show \(t^2+7t+12\). Which rectangle sides are correct?MediumLevel 69If a square model is divided according to side lengths a and b and contains one square of area a², one square of area b², and two equal rectangles each of area ab, which algebraic identity does it represent?MediumLevel 69In the visual model of a square of side a+b formed using parts of lengths a and b, which statement is correct?MediumLevel 69Which arrangement of shapes represents
a^2+2ab+b^2
in a square model?MediumLevel 69A square model shows (c^2-12c+36). What will be its side?MediumLevel 69In a square of side (4x+3), what will be the area of the small corner?MediumLevel 69