Use of Identities in Factorization MCQs Quiz | Class 9

This quiz is designed for Class IX students covering Mathematics (Code 041) Unit II: Algebra. It specifically focuses on the topic “Use of Identities in Factorization”, testing your ability to factorize expressions using standard algebraic identities. Complete the 10 multiple-choice questions below, submit your answers to check your score, and download the detailed PDF answer sheet for your revision.

Algebraic Identities and Factorization Overview

Factorization is the process of writing an algebraic expression as a product of its factors. In Class 9 Algebra, using standard identities is a key method for factorizing polynomials efficiently. Instead of splitting terms manually, we recognize patterns that match specific formulas.

Key Standard Identities

Memorizing these identities is crucial for solving factorization problems quickly:

  • Square of a Binomial: (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
  • Square of a Trinomial: (x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx
  • Sum of Cubes: x^3 + y^3 = (x + y)(x^2 – xy + y^2)
  • Difference of Cubes: x^3 – y^3 = (x – y)(x^2 + xy + y^2)

Steps to Factorize Using Identities

  1. Observe the Terms: Check if the expression has 2, 3, or more terms.
  2. Match the Pattern: Look for perfect squares or cubes. For example, if you see two perfect squares separated by a minus sign, use the difference of squares identity.
  3. Verify the Middle Term: For trinomials like ax^2 + bx + c, check if the middle term matches 2ab (for perfect squares) or use the splitting method if it fits (x+a)(x+b).
  4. Apply the Formula: Rewrite the expression in the factorized form directly.

Extra Practice Questions

Try solving these additional problems to strengthen your understanding:

  1. Factorize: 4x^2 + 12x + 9
  2. Factorize: 100 – 9x^2
  3. Factorize: x^2 + 9x + 18
  4. Expand: (3a – 2b)^2
  5. Find the value of 103 x 107 using identities.