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 identities expresses the difference of two squares as a product of two binomials?MediumLevel 63Which of the following algebraic identities shows the correct factorisation of the difference of two squares?MediumLevel 63What is the value of ( (5x+1)^2-(5x-1)^2 )?MediumLevel 63Which of the following expressions is the factorised form of the difference of two squares, \(a^2-b^2\)?MediumLevel 63Which of the following expressions is an example of the difference of two squares identity?MediumLevel 63What is the value of ( (a+b)^2-(a^2+b^2) )?MediumLevel 63What is the simplified form of ( (a-b)^2-(a^2+b^2) )?MediumLevel 63In which of the following algebraic identities is the middle term negative?MediumLevel 63Which of the following algebraic identities represents the factorisation of the difference of two squares?MediumLevel 63Which identity applies to the product of two binomials having the same terms but opposite signs for the second term?MediumLevel 63What is the general expansion of ( (x+a)(x+b) )?MediumLevel 63What is the coefficient of (x) in ( (2x+1)(2x+7) )?MediumLevel 63What is the coefficient of (a) in ( (3a-2)(3a+8) )?MediumLevel 63What is the simplified form of ( (a+b+c)^2-(a^2+b^2+c^2) )?MediumLevel 63What is the (xz)-term in \( (x+2y-3z)^2 \)?MediumLevel 63What will be the (pq)-term in ( (2p-3q+r)^2 )?MediumLevel 63What is the factor form of ( 64x^2-1 )?MediumLevel 63Which is the correct factor form of ( 121-4y^2 )?MediumLevel 63What is the simplified form of ( (x+6)(x-6)+36 )?MediumLevel 63What is the simplified form of ( (3x+4)^2-(3x-4)^2 )?MediumLevel 63