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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 total (ab)-term in ( (a+b)^2+(b+c)^2+(c+a)^2 )?HardLevel 64What is the simplified form of ( (x+y)^2-(x-y)^2+ (x+2y)^2-(x-2y)^2 )?HardLevel 64What is the simplified form of ( (2x-5)(2x+5)+25 )?HardLevel 64What is the value of \( (x+3)^2+(x+4)^2-2(x+3)(x+4) \)?HardLevel 64What is the simplified form of \( (3a+2b)^2-(3a-2b)^2 \)?HardLevel 64Which of the following polynomials is always non-negative for every real value of \(x\)?HardLevel 64Which of the following pairs of binomials is a pair of conjugates whose product is obtained using the difference of squares identity?HardLevel 64Using identity, what is the value of ( (x+y+z)^2 ) if (x=1), (y=2), (z=3)?HardLevel 64For real numbers \(p\) and \(q\), which of the following expressions can never be negative?HardLevel 64What is the coefficient of (x^2) in the expansion of ( (x+1)(x+2)(x+3) )?HardLevel 64What will be the coefficient of \(x^2\) in ( (x-2)(x+3)(x+5) )?HardLevel 64What is the simplified form of \( (x+2y)^2-(x^2+4y^2) \)?HardLevel 64Which of the following trinomials is equivalent to the expansion of \((2x+3y)^2\) and is therefore a perfect-square trinomial?HardLevel 64Which of the following statements shows the correct use of the identity for the difference of squares?HardLevel 64What is the perfect square form of ( 64x^2+80x+25 )?HardLevel 64\( 25m^2-70mn+49n^2 \) is the square of what?HardLevel 64What is the simplified form of \( (x+a)(x-a)(x^2+a^2) \)?HardLevel 64What is the simplified form of \( (2x+3y)^2+(2x-3y)^2-(8x^2) \)?HardLevel 64What is the simplified form of ( (x+5)(x-3)+(x-5)(x+3) )?HardLevel 64What is the simplified form of ( (x+5)(x-3)-(x-5)(x+3) )?HardLevel 64