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 ( (x+y)^2-(x^2+y^2) ) equal to?MediumLevel 64What is the simplified form of ( (x-y)^2-(x^2+y^2) )?MediumLevel 64What is the value of ( (a+b+c)^2-(a^2+b^2+c^2) )?MediumLevel 64Which is the expansion of ( (x+4)(x-9) )?MediumLevel 64What is the coefficient of (x) in ( (x-8)(x-3) )?MediumLevel 64What is the correct factor form of ( x^2-144 )?MediumLevel 64Which algebraic identity expresses the product of the sum and difference of two terms as the difference of their squares?MediumLevel 64In ( (2a+b+c)^2 ), which mixed terms come besides (2bc)?MediumLevel 64If ( (x+5)^2-(x-5)^2 ) is (80), what is (x)?MediumLevel 64If ( (x+3)^2=x^2+kx+9 ), what is the value of (k)?MediumLevel 64Which of the following equations is an algebraic identity for all real numbers x and y?MediumLevel 64Which of the following algebraic identities is used to factorise the expression \(49m^2-25n^2\)?MediumLevel 64What is the simplified form of ( (4a-5)^2-(16a^2+25) )?MediumLevel 64Which of the following is the correct factorised form of a difference of two squares?MediumLevel 64What is the value of \( 58\times42 \) using ( (50+8)(50-8) )?MediumLevel 64What is the coefficient of (x) in ( (x+a)(x+b) )?MediumLevel 64What is the constant term in ( (x-2)(x+11) )?MediumLevel 64What is the expansion of ( (2x+3)(2x-7) )?MediumLevel 64What is the difference between ( (a+b)^2 ) and (a^2+b^2)?MediumLevel 64What is the difference between ( (a-b)^2 ) and (a^2-b^2)?MediumLevel 64