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
Inside a square of side (x+4), a square of side (x-4) is drawn. What is the difference of the two areas?HardLevel 66Which of the following partitions is correct in a visual model of the identity \((a+b)^2\)?HardLevel 66An area model has to read (81-18x+x^2) as a square. Which is the correct side?HardLevel 66If in a square model \(x^2+ax+36\) is a perfect square and (a) is positive, what is the value of (a)?HardLevel 66If the visual model of (4x^2+kx+49) is a perfect square and the middle term is positive, what is (k)?HardLevel 66In the model of a square with side (2a+3b), what is the total area of the two (ab)-type rectangles?HardLevel 66If a visual model is made for a square of side (5a-2b), what will be the expansion?HardLevel 66In which situation does the area model show (a^2-b^2) instead of (a^2+2ab+b^2)?HardLevel 66In a visual model, the area of ((x+a)(x+b)) is (x^2+9x+20). What can be the values of (a) and (b)?MediumLevel 66If the area model forms the complete square (x^2-12x+36), what is considered the total area of the two removed rectangles?HardLevel 66In the visual model of a square with side (2x+3), what will be the total area of the two equal rectangles?HardLevel 67If a square model shows (9x^2), two (6x) rectangles, and a small square (4), what will be the outer side?HardLevel 67In the model of a square with side (a-b), why is (b^2) added after removing two (ab) strips from (a^2)?HardLevel 67In which rearrangement is the area (a^2-b^2) shown as the rectangle ((a+b)(a-b))?HardLevel 67In the rectangle model of ((x+2y)(x-2y)), what happens to the middle rectangular terms?HardLevel 67If (x^2+10x+25) is made as a complete square using tiles, what is the area of each of the two equal rectangles?HardLevel 67Which expansion is correct in the area model of a square with side (3p-4)?HardLevel 67In a visual model, the large square is (16x^2) and the removed small square is (25). What will be the rectangle dimensions after rearrangement?HardLevel 67If the square model of ((x+a)^2) has small square (49) and total area of two rectangles (14x), what is (a)?HardLevel 67In the rectangle model of ((x+3)(x+8)), which is the correct group of four parts?HardLevel 67