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Algebraic Identities

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsFrom 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?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Expert MathematicsA 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?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Expert MathematicsIn 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?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsA 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?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsA square visual model is divided into one large square, one small square, and two rectangles of equal area. If the areas of these parts are \(a^2\), \(b^2\), and \(ab,ab\) respectively, which algebraic identity does the model represent?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsIf the areas of squares with sides (a+b) and (a-b) are subtracted, which area is obtained visually?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsIn a square visual model, each side is divided into two parts, \(p\) and \(q\). The four regions have areas \(p^2\), \(pq\), \(pq\), and \(q^2\). Which algebraic identity does this model represent?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsA square has side \(p+q\). It is divided into one square of area \(p^2\), one square of area \(q^2\), and two equal rectangles of area \(pq\) each. Which identity does this visual model represent?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsIn a rectangular area model, the length is \(x+y\) and the breadth is \(x-y\), where \(x>y\). Which algebraic identity does this model represent?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsA square visual model is divided into four regions: one square of area \(a^2\), another square of area \(b^2\), and two congruent rectangles each of area \(ab\). Which algebraic identity does this model represent?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsIn a visual model of the algebraic identity \((a+b)^2=a^2+2ab+b^2\), how is the \(2ab\) part usually represented?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsIn a visual model, two strips of width \(b\) are removed from a square of side \(a\). When the common \(b\times b\) corner is added back once, which identity is represented, where \(a>b\)?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsIn a square tile model, one \(x^2\) tile, two \(xy\) rectangular tiles, and one \(y^2\) tile together represent which algebraic identity?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 68Hard MathematicsIn a visual proof, ( (a+b)(c+d) ) is divided into four small rectangles. Which decomposition is correct?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 67Expert MathematicsIf a model is made for a square of side (3a-2b), which final expansion is correct?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 67Expert MathematicsIn a square area model, a large square is divided into four parts: one region has area \(x^2\), two equal rectangles each have area \(xy\), and one small square has area \(y^2\). Which algebraic identity does this model represent?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 67Expert MathematicsIf ( (x-4)(x+9) ) is expanded by a signed tile model, what constant corner is obtained?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 67Expert MathematicsIf a square model of (x+12) gives \(x^2\) and a corner (144), which part will complete the model?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 67Expert MathematicsIn a square model of (u+v+w), what will be the total area of the mixed rectangles?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 67Expert MathematicsIf a square of side (a+b+c) is cut into three parts to make a model, how many rectangles of type (ab) will appear?Class 9Exploring Algebraic IdentitiesVisual models of identitiesLevel 67Expert