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Mathematics

Algebraic identities

बीजीय सर्वसमिकाएँ

In this Class 9 Mathematics topic from “Exploring Algebraic Identities,” students learn how standard algebraic relationships remain true for all permitted values of the variables. They study and apply identities such as (a + b)², (a − b)², and a² − b² to expand expressions, simplify calculations, and factorise algebraic forms. The topic also develops skill in recognising suitable patterns, substituting values to verify results, and using identities to solve expressions efficiently and accurately.

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DifficultyAll difficultiesExpertLevelAll levelsLevel 64Timer20 minutes10 minutes30 minutesNo timer

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1. Which algebraic identity is used to factorise the difference of two cubes, \(a^3-b^3\)?Expert · Level 64 · algebraic identities,difference of cubes,factorisation,class 9 mathematics,polynomials

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1. \(a^3-b^3=(a-b)(a^2+ab+b^2)\)
2. \(a^3+b^3=(a+b)(a^2-ab+b^2)\)
3. \(a^2-b^2=(a-b)(a+b)\)
4. \((a-b)^3=a^3-3a^2b+3ab^2-b^3\)

2. Which of the following factorisation identities is correct for all real values?Expert · Level 64 · algebraic identities,difference of cubes,factorisation,class 9 mathematics,polynomial identities

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1. \(a^3-b^3=(a-b)(a^2-ab+b^2)\)
2. \(a^3-b^3=(a+b)(a^2-ab+b^2)\)
3. \(a^3-b^3=(a-b)(a^2+ab+b^2)\)
4. \(a^3-b^3=(a-b)(a^2+ab-b^2)\)

3. Which is the simplified form of ( (2x+y+3)^2-(2x-y+3)^2 )?Expert · Level 64 · grouping identity,square difference,three terms

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1. (4y(2x+3))
2. (2y(2x+3))
3. (4x^2-y^2+9)
4. (8xy+6y)