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 is a perfect-square trinomial for all real values of the variables?HardLevel 65Which of the following expressions can be directly identified as a difference of two perfect squares?HardLevel 65Which is the correct expansion of ( (x-3)^3 )?HardLevel 65What is the correct expansion of ( (2x+3)^3 )?HardLevel 65Which of the following trinomials can be written as the product of two identical binomial factors?HardLevel 65What is the correct factorisation of (125p^3-8q^3)?HardLevel 65Which of the following polynomials is the expansion of \((a+b)^3\)?HardLevel 65Which of the following trinomials can be written as the square of a binomial for all \(p\) and \(q\)?HardLevel 65Which of the following trinomials is the expansion of the square of a binomial?HardLevel 65If (a+b+c=9) and (a^2+b^2+c^2=35), what is (ab+bc+ca)?HardLevel 65What is the sum of the terms containing (xy), (yz), and (xz) in ( (2x+3y+z)^2 )?HardLevel 65What is the safest strategy while using an algebraic identity?HardLevel 65If a trinomial is of the form \(u^2-2uv+v^2\), which of the following algebraic identities does it represent?HardLevel 65Which of the following expressions gives \(a^2+b^2+c^2+2ab+2bc+2ca\) when expanded?ExpertLevel 62Which is the (bc)-term in ( (3a-2b+c)^2 )?ExpertLevel 62Which of the following polynomials can be written as the perfect square of a binomial?ExpertLevel 62Which of the following expressions is in the form of a difference of two squares, \(a^2-b^2\)?ExpertLevel 62Which of the following algebraic identities has \(+2ab\) as the middle term in its expansion?ExpertLevel 62Which of the following polynomials can be identified as the square of a binomial?ExpertLevel 62A student claims that \(1003^2=1000^2+3^2=1000009\). What is the correct value of \(1003^2\) when the algebraic identity is applied correctly?ExpertLevel 62