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Subjects

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+y)^2-(x-y)^2-4xy)?MediumLevel 63In ( (a+2b+c)^2 ), what is the sum of the terms containing (bc) and (ac)?HardLevel 63Which of the following expressions can be factorised as the perfect square of a binomial?HardLevel 63What is the value of ( (x+2)(x+5)-(x+3)(x+4) )?HardLevel 63What are the coefficient of (x) and the constant term in ( (x-8)(x+2) )?HardLevel 63Choose the correct value of ( 1005^2-995^2 ).HardLevel 63Which of the following expressions is identically equal to \((a+b)^2\) for every real number a and b?HardLevel 63Which of the following identities gives the correct factorised form of the sum of two cubes?HardLevel 63What is the simplified form of ( (7a+1)^2-(7a-1)^2 )?HardLevel 63Which of the following algebraic identities gives the standard form of the product of two binomials that differ only in the sign of the second term, such as \\(p+q\\) and \\(p-q\\)?HardLevel 63Which of the following expressions represents the expansion of \((x+y)^2\)?HardLevel 63What is the value of ( (x+y)^2+(x-y)^2-2x^2 )?HardLevel 63What is the value of ( (3p+q)^2-(3p-q)^2-12pq )?HardLevel 63What is obtained by simplifying ( (x+2y)^2-x^2-4y^2 )?HardLevel 63Which of the following quadratic polynomials has integer factors that are two linear binomials with constant terms of opposite signs?HardLevel 63Which is the factorisation of (16a^2-40ab+25b^2)?HardLevel 63When first applying ( (x+1)(x+3) ) in ( (x+1)(x+2)(x+3) ), what form is obtained?HardLevel 63What is the full expansion of ( (x+1)(x+2)(x+3) )?HardLevel 63Which is the correct expansion of ( (a+b)^3 )?HardLevel 63Which of the following expressions is a perfect square of the sum of two terms?HardLevel 63