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 a square model has corner squares (x^2) and (64), what combined middle term is needed to form a perfect square?HardLevel 68Why does the (xy) term not remain when a rectangle with sides (x+y) and (x-y) is expanded in an area model?HardLevel 68In a square model, (m^2+2mn+n^2=196). If the outer side (m+n) is positive, what is (m+n)?HardLevel 68If a rectangle model represents ((x-6)(x+2)), what is the sign and value of the combined (x)-term?HardLevel 68A side of a square is divided into two parts, x and y. The visual model contains one square of area x², one square of area y², and two rectangles each of area xy. Which algebraic identity does this model represent?HardLevel 68Inside a square, corner parts (x^2) and (81) are shown. If the total area is (x^2-18x+81), what is the side of the model?HardLevel 68If the areas of two squares are (121) and (49), what is the area of the visual rectangle for their difference?HardLevel 68In an area model of a square of side \(a\), two \(ab\) rectangles are removed and their common \(b^2\) part is added back once. Which identity does this visual model represent?HardLevel 68If in the model of ((a+b)^2), (a^2=64), (b^2=36), and both are positive, what is the combined rectangular area (2ab)?HardLevel 68A visual model shows three areas ((x+y)^2), ((x-y)^2), and (4xy). Which relation is correct?HardLevel 68A square visual model first has side (a). A strip of width (b) is added on the right and another strip of width (b) at the bottom with a small corner square. Which identity does the total area show?ExpertLevel 68From a large square of side (p), two strips of width (q) are removed from the top and the right. The corner square (q^2) is added back because it was removed twice. What is the remaining area?ExpertLevel 68A rectangle has length (x+7) and width (x+3). When it is split into (x^2) square tiles and linear strips, what will be the coefficient of the middle term?ExpertLevel 68A square of side (m+n) is divided into four parts. Two parts have areas (m^2) and (n^2). What is the combined area of the remaining two equal rectangles?ExpertLevel 68In a visual model, a small square of area (s^2) is removed from a square of area (r^2). The remaining L-shape is cut and rearranged into a rectangle. What will be the sides of that rectangle?ExpertLevel 68A square (x) by (x), four strips (x) by (2), and four small squares (2) by (2) form one larger square. What is the side of the larger square?ExpertLevel 68If a square model shows total area (x^2+12x+36), what is the side of that square?ExpertLevel 68In a square model, the combined area of two equal rectangles is (18xy) and the small corner square is (81y^2). If the main square is (x^2), what is the complete square area?ExpertLevel 68In a visual proof, a square of side (a+b+c) is divided into nine parts. Three square parts have areas (a^2), (b^2), and (c^2). What is the total area of the rectangular parts?ExpertLevel 68A tile model arranges (x^2+11x+30) as a rectangle. If one side is (x+5), what will be the other side?ExpertLevel 68