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Subjects

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.

Practice questions

Which of the following expressions is always a perfect-square trinomial?ExpertLevel 62If ( (3m+n)^2-(3m-n)^2=48mn ), what is (m) for (n\neq0)?ExpertLevel 62What is the simplified form of ( (x+4)(x-6)+(x-4)(x+6) )?ExpertLevel 62What is the simplified form of ( (x+4)(x-6)-(x-4)(x+6) )?ExpertLevel 62What will be the coefficient of (x^2) in ( (x-2)(x+5)(x-7) )?ExpertLevel 62What is the constant term in ( (x+1)(x-3)(x+8) )?ExpertLevel 62Which of the following expressions can be factorised using the identity for the sum of cubes?ExpertLevel 62Which of the following algebraic identities gives the factorised form of the difference of two squares?ExpertLevel 62Which of the following expressions represents the expansion of \((a+b)^2\)?ExpertLevel 62The product of which two binomials is written as a difference of squares?ExpertLevel 62If two binomials have the same terms, but one has a plus sign and the other has a minus sign between them, which algebraic form is their product equal to?ExpertLevel 62What is the value of ( 1004^2-996^2 )?ExpertLevel 62Using identity, what is the value of ( 503^2+497^2 )?ExpertLevel 62What is the value of ( 203^2-197^2 )?ExpertLevel 62What is the simplified factor form of ( (x^2+1)^2-x^4 )?ExpertLevel 62Which of the following trinomials is a perfect square of the difference of two binomials?ExpertLevel 62What is the constant term in the full expansion of ( (x+1)(x+2)(x+3) )?ExpertLevel 62What will be the constant term in ( (2x+1)(2x-3)(2x+5) )?ExpertLevel 62Which of the following trinomials represents the standard expansion of \((a+3b)^2\)?ExpertLevel 62Why can ( (4x+y)^2-(4x-y)^2 ) be written equal to (32xy)?ExpertLevel 62