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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

What is the simplified form of ( (2x-1)(2x+7)-(2x+1)(2x+5) )?ExpertLevel 62Which of the following expressions can be factorised by applying the standard identity for the difference of squares twice in succession?ExpertLevel 62If ( (x+y)^2=81 ) and (xy=14), what is the value of (x^2+y^2)?ExpertLevel 63Which of the following expressions is the square of a sum of two terms?ExpertLevel 63Which of the following expressions can be classified as a difference of two squares?ExpertLevel 63Simplify ( (5a-2b)^2-(25a^2+4b^2) ).ExpertLevel 63If ( (x+k)^2=x^2+24x+144 ), what is the value of (k)?ExpertLevel 63If ( (x-k)^2=x^2-30x+225 ), what is (k)?ExpertLevel 63What is the value of ( (3x+4)(3x-4)-(9x^2-20) )?ExpertLevel 63Which term containing (yz) appears in ( (x+2y+3z)^2 )?ExpertLevel 63Which of the following trinomials is a perfect square of a binomial?ExpertLevel 63If ( (x+y)^2-(x-y)^2=72 ), what is the value of (xy)?ExpertLevel 63Which of the following identities has the cross term \(-2pq\) in its expansion?ExpertLevel 63What is the value of ( 1005^2-995^2 ) using an identity?ExpertLevel 63What do we get for \( 123\times117 \) using an identity?ExpertLevel 63What is the value of ( 998^2 ) using ( (1000-2)^2 )?ExpertLevel 63Which of the following expressions is a correct example of the identity for the difference of two squares?ExpertLevel 63What is the value of ( (x+3)(x+8)-(x+4)(x+7) )?ExpertLevel 63What is the coefficient of (x) in ( (2x+5)(2x-3) )?ExpertLevel 63What is the constant term in ( (3x-2)(3x+6) )?ExpertLevel 63