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 coefficient of (x^2) in ( (x-1)(x-2)(x-3) )?ExpertLevel 63What is the simplified form of ( (a+b)^3-(a-b)^3 )?ExpertLevel 63What is ( (a+b)^3+(a-b)^3 ) equal to?ExpertLevel 63Which of the following expressions can be written using the identity for the difference of two cubes?ExpertLevel 63If, for real constants p and q, the expression \(x^2+px+q\) can be written as the perfect square of a binomial involving \(x\) and a constant, which relation between \(p\) and \(q\) is necessary?ExpertLevel 63If (a+b+c=0), what is (a^3+b^3+c^3) equal to?ExpertLevel 63If (x+y+z=0), what is the value of ( x^3+y^3+z^3-3xyz )?ExpertLevel 63Which of the following expressions is divisible by \,a-b\, for all values of the variables?ExpertLevel 63What remains when (x^2+y^2+z^2) is removed from ( (x+y+z)^2 )?ExpertLevel 63What is the simplified form of ( (2x+3)^2-(2x+3)(2x-3) )?ExpertLevel 63What will be the term containing (x^2) in ( (x+4)^3-(x-4)^3 )?ExpertLevel 63What is the simplified form of ( (x+2)^3+(x-2)^3 )?ExpertLevel 63What is the simplified form of ( (a+b)^2-(a^2-b^2) )?ExpertLevel 63What is ( (a-b)^2-(a^2+b^2) ) equal to?ExpertLevel 63Which of the following expressions is always non-negative for all real values of \(x\) and \(y\)?ExpertLevel 63If (t-\frac{1}{t}=6), what is (t^2+\frac{1}{t^2})?ExpertLevel 63What is the value of ( (x+\frac{1}{x})^2-(x-\frac{1}{x})^2 )?ExpertLevel 63What is the simplified form of ( (x-2)(x+2)(x^2+4) )?ExpertLevel 63Which of the following algebraic identities expresses the product of the sum and difference of two terms as the difference of their squares?ExpertLevel 63Which of the following expressions can be factorised directly using the difference of squares identity \(A^2-B^2=(A-B)(A+B)\)?ExpertLevel 63