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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

Which of the following algebraic identities is true for every real value of a and b?MediumLevel 64If (x+y+z=6) and (xy+yz+zx=11), what is the value of (x^2+y^2+z^2)?HardLevel 63Which is the correct factorisation of (8x^3+27)?HardLevel 63What is the simplified form of ( (2x+3y)^2+(2x-3y)^2 )?HardLevel 64What is the simplified form of ( (4a+b)^2-(4a-b)^2 )?HardLevel 64( 9x^2-30x+25 ) is the perfect square of what?HardLevel 64Which of the following expressions can be identified as the square of a sum of two positive terms?HardLevel 64Which is the correct factor form of ( 121a^2-49b^2 )?HardLevel 64What is the coefficient of (x) in ( (3x-4)(3x+7) )?HardLevel 64What is the simplified form of ( (x+4)(x-9)-x^2 )?HardLevel 64For two algebraic expressions \(U\) and \(V\), which part remains unchanged in the expansions of \((U+V)^2\) and \((U-V)^2\)?HardLevel 64Which of the following expressions can be identified as the square of a binomial?HardLevel 64What is the value of ( 1008^2-992^2 )?HardLevel 64Using identity, what is the value of \( 997^2 \)?HardLevel 64Which of the following expressions is not generally a perfect square of a binomial?HardLevel 64Which of the following polynomials can be written as the square of the sum of three variables?HardLevel 64What is the simplified form of ( (5m-2n)^2-(5m+2n)^2 )?HardLevel 64Which of the following equalities represents the algebraic identity for the difference of two squares?HardLevel 64Which of the following trinomials can be identified as the square of a binomial?HardLevel 64What is the correct expansion of the first two factors in ( (x+6)(x-4)(x+1) )?HardLevel 64