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
A square tile model shows (z^2+6z+9). What is the side of the complete square?EasyLevel 69A rectangle has length (a+5) and breadth (a-5). Which area does the visual model show?EasyLevel 69If two equal rectangles in an area model have areas 7x and 7x, what is the total middle term?EasyLevel 69A square visual model is divided into one large square, a square of side x, a square of side y, and two equal rectangles of dimensions xy. Which algebraic identity does this model represent?EasyLevel 69A square model shows parts \(x^2\), (12x), and (36). What side of the square does it indicate?EasyLevel 69In the rectangle model of ((p+2)(p+5)), what is the area of the small corner rectangle?EasyLevel 69Which expansion is given by the area model of a square with side (a+2b)?EasyLevel 69In a visual model, the rectangular form of (c^2-d^2) is equal to what?EasyLevel 69Each side of a square model is divided into parts x and y. The model contains one square of area x², one square of area y², and two rectangles of area xy. Which algebraic identity does this model represent?EasyLevel 69In the model of a square with side (t-3), what will be the last term?EasyLevel 69In an area model, the four parts of a rectangle are (u^2), (2u), (5u), and (10). Which product does the whole rectangle show?EasyLevel 69A square model shows \(4x^2+12x+9\). What will be its side?EasyLevel 69In a square with side (a+b), what shape is the (a^2) part?EasyLevel 69If the side of a square is (x+2), which part will not appear among its four regions?EasyLevel 69In a visual model, when a square of side (b) is removed from a square of side (a), what is the remaining area called?EasyLevel 69In a rectangle model, the length is (x+6) and the breadth is (x). What is the area?EasyLevel 69While making a square model of side (s+4), how many (4s) rectangles appear besides (s^2)?EasyLevel 69Which area model has the whole square (a^2) and the inner remaining square ((a-b)^2)?EasyLevel 69In a tile model of a square with side \(x+y\), there is one \(x^2\) square, one \(y^2\) square, and two \(xy\) rectangles. Which algebraic expression does this model represent?EasyLevel 69In a square model with side (a+b), in which form is the total area directly obtained from the outer boundary?EasyLevel 69