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 expansion of ( (x+2)^3 )?HardLevel 63Which is the correct expansion of ( (2x-1)^3 )?HardLevel 63What is the factorisation of ( a^3+b^3 )?HardLevel 63What is ( a^3-b^3 ) equal to?HardLevel 63Choose the factorisation of ( 27x^3+8y^3 ).HardLevel 63What is the correct factorisation of ( 64m^3-125n^3 )?HardLevel 63What is the simplified form of ( (a+b)^3-(a^3+b^3) )?HardLevel 63Which is the correct algebraic identity for factorising the sum of two cubes?HardLevel 63Which of the following is the algebraic identity for the square of a sum of three terms?HardLevel 63If (a-b=6) and (ab=16), what is (a^2+b^2)?HardLevel 63Which of the following identities correctly represents the expansion of the square of a sum of three terms?HardLevel 63If (m+n=12) and (m-n=4), what is the value of (mn)?HardLevel 63What will be the term containing (x^2) in ( (x+5)^3-(x-5)^3 )?HardLevel 63What is the complete simplified form of ( (x+5)^3-(x-5)^3 )?HardLevel 63Which of the following binomials is a factor of \(x^3+8y^3\)?HardLevel 63Choose the correct coefficient of (a^2b) in ( (2a+b)^3 ).HardLevel 63Simplify ( (a+b+c)^2-(a^2+b^2+c^2+2ab) ).HardLevel 63In ( (x+2y+3z)^2 ), what do the (xz) term and the (yz) term together form?HardLevel 63In which situation can ( (a+b)^2=a^2+b^2 ) be true?HardLevel 63What is the simplified form of ( (2x+y)^2-(2x-y)^2 )?MediumLevel 64