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 sum of the terms containing (xy), (yz), and (xz) in ( (x+3y+4z)^2 )?ExpertLevel 64Which form is most suitable for finding (998^2) using an identity?ExpertLevel 64What is the correct value of (998^2)?ExpertLevel 64What is the value of (1006^2-994^2)?ExpertLevel 64Which of the following correctly represents the factorised form of
a^2-b^2
?ExpertLevel 64What is the simplified form of ( (8x+1)^2-(8x-1)^2 )?ExpertLevel 64Which of the following expressions can be factorised directly using the identity \(a^2-b^2=(a-b)(a+b)\)?ExpertLevel 64Which of the following expressions is a difference of two perfect-square terms and can therefore be factorised using the identity \((a+b)(a-b)=a^2-b^2\)?ExpertLevel 64What is the coefficient of the term containing (a^2b) in ( (4a-b)^3 )?ExpertLevel 64Which of the following expressions is the correct factorisation of the sum of two cubes?ExpertLevel 64Which of the following expressions is the correct form of the identity for the difference of two cubes?ExpertLevel 64Choose the correct factorisation of (27p^3-64q^3).ExpertLevel 64Which of the following expressions is a factor of the sum of two cubes?ExpertLevel 64Which of the following shows the correct perfect-square factorisation of \(p^2-2pq+q^2\)?ExpertLevel 64Which of the following expressions does not occur in the expansion of \((a+b)^3\)?ExpertLevel 64If (m+n=14) and (m^2+n^2=100), what is (mn)?ExpertLevel 64Which of the following expressions is equal to the square of the difference of two terms, \((x-y)^2\)?ExpertLevel 64Which of the following expressions represents the correct expansion of \((a-b)^3\)?ExpertLevel 64What is the full expansion of ( (x+3)(x+5)(x+7) )?ExpertLevel 64When first applying ( (2x+1)(2x+9) ) in ( (2x+1)(2x+5)(2x+9) ), what is obtained?ExpertLevel 64