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 has side \(a+b\). Which identity is shown by its area model?EasyLevel 68A diagram has two small squares with sides \(a\) and \(b\) and two equal rectangles. What is the total area?EasyLevel 68If the side of a big square is \(x+3\), how will its area be written?EasyLevel 68A square has side \(a\). A corner square of \(b \times b\) is removed. The remaining area is related to which expression?EasyLevel 68In a visual model \(a^2-b^2\) is rearranged into two rectangles. Which factorisation does it show?EasyLevel 68What is the area of a square with side \(a-b\)?EasyLevel 68In a diagram two \(a \times b\) rectangles are subtracted from a big \(a \times a\) square and a \(b \times b\) square is added back. Which identity is formed?EasyLevel 68What is the area of a rectangle with length \(x+2\) and breadth \(x+5\) in visual form?EasyLevel 68In a tile model there is one \(x^2\) tile and \(8\) \(x\)-tiles. If there are \(16\) constant tiles then the complete square models what?EasyLevel 68If in a square model the total area of the two middle rectangles is \(10x\) and the small square area is \(25\), what is the side?EasyLevel 68In the visual model of \((p+q)^2\), how many \(pq\) rectangles are formed?EasyLevel 68A square with sides \(m+n\) and \(m+n\) is split into four parts. Which part is not formed?EasyLevel 68A rectangle has length \(a+b\) and breadth \(a-b\). Its area is equal to what?EasyLevel 68If \(7 \times 9\) is viewed as \((8-1)(8+1)\) in a visual model, what is its value?EasyLevel 68Using a visual model, what is the area of a square with side \(10+2\)?EasyLevel 68A square model contains \(6^2\), two \(6 \times 4\) rectangles and a \(4^2\) square. What is the total area?EasyLevel 68If \(99^2\) is found using the model of \((100-1)^2\), what is the correct value?EasyLevel 68In a visual model, \(x^2+12x+36\) can be seen as which perfect square?EasyLevel 68A square made of four parts \(y^2\), \(4y\), \(4y\), and \(16\) shows which expression?EasyLevel 68If the side of a square is \(r+s\), what does \(s^2\) show in its model?EasyLevel 68