Algebraic Expressions & Identities (Recall) MCQs Quiz | Class 9

This Class IX Mathematics (Code 041) quiz focuses on Unit II: Algebra, specifically checking your recall and application of standard algebraic identities used for simplification. Test your skills with these 10 MCQs based on the CBSE curriculum. Submit your answers to see your score and download the comprehensive solution PDF.

Overview of Algebraic Identities

In Class IX Mathematics, Unit II: Algebra places significant emphasis on the understanding and application of algebraic identities. An identity is an equality that holds true for all values of the variables involved. Recalling these standard identities is essential for polynomial factorization, expansion, and simplification tasks.

Key Standard Identities

The following identities are the foundation for this topic:

  • Square of a Sum: (x + y)^2 = x^2 + 2xy + y^2
  • Square of a Difference: (x – y)^2 = x^2 – 2xy + y^2
  • Difference of Squares: x^2 – y^2 = (x + y)(x – y)
  • Product of Binomials: (x + a)(x + b) = x^2 + (a + b)x + ab

Applications in Simplification

These identities are not just theoretical; they allow for rapid calculation and simplification. For example, calculating 102 x 98 becomes simple using the difference of squares: (100 + 2)(100 – 2) = 10000 – 4 = 9996. Similarly, expanding (2a + 3b)^2 uses the first identity, resulting in 4a^2 + 12ab + 9b^2.

Quick Revision Table

Name Identity LHS Identity RHS
Square Sum (a + b)^2 a^2 + 2ab + b^2
Square Diff (a – b)^2 a^2 – 2ab + b^2
Diff of Squares a^2 – b^2 (a + b)(a – b)
General Product (x + a)(x + b) x^2 + (a + b)x + ab

Extra Practice Questions

  1. Find the value of 99^2 using a suitable identity.
  2. Factorize: 25x^2 – 16y^2.
  3. Expand: (3x – 4y)^2.
  4. Evaluate 104 x 105 using (x+a)(x+b).
  5. If x + 1/x = 6, find the value of x^2 + 1/x^2.