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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

If (x+y=9) and (xy=14), what is (x^2+y^2)?MediumLevel 64If (p-q=5) and (pq=6), what is (p^2+q^2)?MediumLevel 64Which algebraic identity is used to express the difference of two squares as a product of factors?MediumLevel 64When simplifying ( (x+1)(x+2)(x+3) ) starting with the first two factors, which middle step is correct?MediumLevel 64What is the simplified form of ( (x+2)^2-(x+2)(x-2) )?MediumLevel 64What is the value of ( (3x+2)^2+(3x-2)^2 )?MediumLevel 64What is the coefficient of (x^2) in ( (2x-5)^2 )?MediumLevel 64What is the coefficient of (y^2) in ( (x+3y)^2 )?MediumLevel 64What is the main difference between ( (x+5)(x-5) ) and ( (x-5)^2 )?MediumLevel 64Which of the following expressions represents the algebraic identity for the square of the sum of two terms?MediumLevel 64Which term containing (ab) appears in ( (a-b+c)^2 )?MediumLevel 64What is obtained by simplifying ( (3a+4b)^2+(3a-4b)^2 )?HardLevel 63Which is the simplified form of ( (x+y+z)^2-x^2-y^2-z^2 )?HardLevel 63What is the value of ( x^2+14x+49-(x+7)^2 )?HardLevel 63Simplify ( (a+b)^2-(a^2+b^2) ).HardLevel 63What is the correct expansion of ( (x+4)(x-6) )?HardLevel 63If the expression \(x^2+px+q\) can be written as \((x+r)^2\) for some real number \(r\), which relation between \(p\) and \(q\) is necessary and sufficient?HardLevel 63What is the factorisation of (25p^2-36q^2)?HardLevel 63Which of the following trinomials represents the expansion of \((x+5y)^2\)?HardLevel 63Which of the following trinomials is not a perfect square trinomial?HardLevel 63