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 ( (6x+1)^2-(6x-1)^2 )?HardLevel 65Which of the following is the correct factorised form of \(a^3+b^3+c^3-3abc\)?HardLevel 65Which of the following expressions can be written as a product of two binomials using the identity for the difference of two squares?HardLevel 65What is the coefficient of the term containing (a^2b) in ( (3a-b)^3 )?HardLevel 65What is the complete simplified form of ( (x+4)^3-(x-4)^3 )?HardLevel 65Which of the following expressions can be identified as a perfect-square trinomial?HardLevel 65Choose the correct factorisation of ( 64x^3-27y^3 ).HardLevel 65How will ((a+b)^3-(a^3+b^3)) be written in factor form?MediumLevel 65Which of the following expressions matches the identity for the square of a difference,
\((p-q)^2=p^2-2pq+q^2\)?HardLevel 65If (x+y=13) and (xy=40), what is the value of (x^2+y^2)?HardLevel 65Which of the following expressions is a factor of \(x^3+8\)?HardLevel 65Which of the following pair of factors uses the identity for the difference of squares?HardLevel 65Which of the following identities correctly represents the square expansion of \,\((a+b+c)^2\)?HardLevel 65Which of the following statements correctly represents the identity for the difference of two squares?HardLevel 65Which of the following terms does not appear in the expansion of \((a-b)^3\)?HardLevel 65When first applying ( (2x+1)(2x+5) ) in ( (2x+1)(2x+3)(2x+5) ), what is obtained?HardLevel 65What is the full expansion of ( (x+2)(x+4)(x+6) )?HardLevel 65Which of the following expressions represents the expansion of \((a+b-c)^2\)?HardLevel 65Which of the following trinomials can be factorised directly using a perfect-square identity?HardLevel 65Let \(a,b,c\) be real numbers. Which of the following expressions can always be written as the perfect square of a trinomial?HardLevel 65