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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.

Practice questions

When starting ( (x+1)(x+2)(x+3) ) with the first two factors, which intermediate form is correct?MediumLevel 63 What will be the coefficient of (x) in ( (2x-3)(2x+9) )?MediumLevel 63 What will be the coefficient of (x) after expanding ( (x-5)(x+11) )?MediumLevel 63 What is the value of ( (2x+5)^2-(2x-5)^2 )?MediumLevel 64 Choose the correct expansion of ( (3a-4b)^2 ).MediumLevel 64 What is the expansion of ( (x+6)(x-2) )?MediumLevel 64 What is the value of ( 104^2-96^2 )?MediumLevel 64 Which of the following algebraic identities has a positive middle term equal to twice the product of the two terms in its expansion?MediumLevel 64 In ( (a+3b+c)^2 ), where does (6ab) come from?MediumLevel 64 What is the linear term containing (x) in ( (2x+y+3)^2 )?MediumLevel 64 Which of the following expressions is a difference of two squares?MediumLevel 64 Which of the following factorizations represents the identity for the difference of two squares?MediumLevel 64 What is ( 87\times93 ) using an identity?MediumLevel 64 Simplify ( (4x-3)(4x+3)+9 ).MediumLevel 64 In ( (x+2)(x+7) ), what are the constant term and coefficient of (x) respectively?MediumLevel 64 What is the factor form of ( x^2-22x+121 )?MediumLevel 64 What is the value of ( (7a+2b)^2-(7a-2b)^2 )?MediumLevel 64 What is the simplified form of ( (2p+3q)^2+(2p-3q)^2 )?MediumLevel 64 Which of the following expressions can be identified as the square of the difference of two terms?MediumLevel 64 What is the value of ( 197^2 ) using an identity?MediumLevel 64