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 value of \( (x+3y)^2-x^2-9y^2-6xy \)?ExpertLevel 64Which of the following expressions is the trinomial form of the square of a sum of two terms?ExpertLevel 64Which statement about the signs of terms in the expansion of \((a-b)^3\) is correct?ExpertLevel 64Which is the correct expansion of ( (x-4)^3 )?ExpertLevel 64What is the correct expansion of ( (3x+4)^3 )?ExpertLevel 64Which of the following polynomials is an example of the difference of squares identity, whose factors differ only in sign?ExpertLevel 64What is the correct factorisation of (216p^3-125q^3)?ExpertLevel 64Which of the following expressions can be factorised as the difference of two perfect cubes?ExpertLevel 64Which of the following expressions can be written as the product of a linear factor and a quadratic factor in the form
\( (a-b)(a^2+ab+b^2) \)?ExpertLevel 64Which of the following expressions does not appear in the expansion of \((x+y+z)^2\)?ExpertLevel 64Which of the following expressions is a perfect-square trinomial and can be written as the square of a binomial?ExpertLevel 64Which of the following expressions can be identified as a difference of two squares without expanding it?ExpertLevel 64What is the simplified form of ( (3x+2)^2-(3x-2)^2+(x+5)(x-5) )?ExpertLevel 64What will be the term containing (ab^2) in ( (4a+b)^3-(4a-b)^3 )?ExpertLevel 64What is the safest check while applying a special algebraic identity?ExpertLevel 64What is the simplified value of ( (x+6)^2-(x+2)(x+10) )?ExpertLevel 63If \(x+\frac{1}{x}=7\), what is the value of \(x^3+\frac{1}{x^3}\)?ExpertLevel 63Which is the correct factor form of (27a^3+8b^3)?ExpertLevel 63If (a+b+c=9) and (ab+bc+ca=20), what is (a^2+b^2+c^2)?ExpertLevel 63What is the simplified form of ( (x+2y)^3+(x-2y)^3 )?ExpertLevel 64