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
Which of the following expressions can be written as the product of the sum and difference of the same two terms?ExpertLevel 62What is the value of ( (2x+7)^2+(2x-1)^2-2(2x+7)(2x-1) )?ExpertLevel 62What is the simplified form of ( (a+b+c)^2-(a^2+b^2+c^2+2ab) )?ExpertLevel 62What is the simplified form of ((x+2y+z)^2-(x^2+4y^2+z^2))?HardLevel 62What is the sum of the (xy)-term and (yz)-term in ( (3x-2y+z)^2 )?ExpertLevel 62What will be the coefficient of (x) in ( (x+4)(x-1)(x-6) )?ExpertLevel 62What is the coefficient of (x) in ( (x+3)(x-4)(x+2) )?ExpertLevel 62What is the coefficient of (x) in ( (2x+1)(2x+3)(2x-5) )?ExpertLevel 62Which of the following expressions is a factor of \(a^4-b^4\)?ExpertLevel 62Which of the following trinomials is a perfect square trinomial?ExpertLevel 62For which of the following products does the difference-of-squares identity apply?ExpertLevel 62Which of the following is a pair of conjugate binomials whose product can be written as a difference of squares?ExpertLevel 62Which of the following expressions can be classified as the square of a sum of two terms?ExpertLevel 62What is the simplified form of ( (4x-5)^2-(16x^2+25) )?ExpertLevel 62Which of the following products has conjugate factors and expands to a difference of two squares?ExpertLevel 62( (x+y+z)^2-(x+y-z)^2=40z ). If (x+y=5), why is this correct?ExpertLevel 62For real numbers \(a\) and \(b\), which of the following expressions is always non-negative?ExpertLevel 62To which of the following expressions can the identity \(a^2-b^2=(a+b)(a-b)\) be applied directly?ExpertLevel 62Which of the following expressions can be factorised in the form of a difference of two squares, \(a^2-b^2\)?ExpertLevel 62What is the simplified form of ( (x+2)(x+6)-(x+3)(x+5) )?ExpertLevel 62