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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 algebraic identity is appropriate for factorising the expression \(49p^2-64q^2\)?ExpertLevel 63Which of the following shows the correct factorisation of the difference of two squares?ExpertLevel 63Which of the following polynomials is a perfect-square trinomial?ExpertLevel 63What is the term containing (xz) in ( (2x-3y+z)^2 )?ExpertLevel 63Which of the following expressions is a perfect-square trinomial for every real value of x?ExpertLevel 63If ( (x-4)(x+k)=x^2+3x-28 ), what is the value of (k)?ExpertLevel 63What is the simplified form of ( (x+3)^2-(x-1)(x+7) )?ExpertLevel 63What is the value of ( (2x+1)(2x+9)-(2x+5)^2 )?ExpertLevel 63Which identity correctly expresses the difference of two squares as a product of factors?ExpertLevel 62What is obtained by simplifying ( (5a-4b)^2+(5a+4b)^2 )?ExpertLevel 64Which is the correct simplified form of ( (x+y+z)^2-(x-y+z)^2 )?ExpertLevel 64What is the sum of the terms containing (pq), (pr), and (qr) in ( (3p+2q+r)^2 )?ExpertLevel 64(16x^2-40xy+25y^2) is the perfect square of what?ExpertLevel 64What is the correct factorisation of (81a^2-49b^2)?ExpertLevel 64What are the coefficient of (x) and the constant term in ( (x+12)(x-5) )?ExpertLevel 64Which of the following pairs of factors represents the factorisation of an expression that is a difference of two squares?ExpertLevel 64What is the value of ( (4m-3n)^2-(16m^2+9n^2) )?ExpertLevel 64What is the value of ( (a+b)^2+(a-b)^2-2a^2-2b^2 )?ExpertLevel 64What is the value of ( (x+4)(x+10)-(x+6)(x+8) )?ExpertLevel 64What is obtained by simplifying ( (3a+b+c)^2-(9a^2+b^2+c^2) )?ExpertLevel 64