Identity Verification: (a+b)^3 MCQs Quiz | Class 9

This Class IX Mathematics (Code 041) quiz focuses on Unit II: Algebra. It covers the topic of verifying and applying the algebraic identity (a+b)^3 for expansion and factorization. Test your understanding of cubic expansions, numerical applications, and coefficient identification. Submit your answers to view the detailed scorecard and download the result PDF.

Understanding the Identity (a + b)^3

The algebraic identity for the cube of a binomial is a fundamental concept in Class 9 Algebra. It is expressed in two common forms:

  • Expanded Form: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
  • Factored Form: (a + b)^3 = a^3 + b^3 + 3ab(a + b)

This identity is derived by multiplying (a + b) by itself three times. It is crucial for solving problems related to expansion of polynomials, factorization of cubic expressions, and finding cubes of large numbers using the splitting method.

Key Applications

Students must learn to verify this identity by substituting values for ‘a’ and ‘b’. For example, if a=2 and b=3, the Left Hand Side (LHS) becomes (2+3)^3 = 125. The Right Hand Side (RHS) is calculated by substituting these values into the expanded formula, which should also equal 125.

Quick Revision Table

Expression Standard Expansion Remarks
(x + y)^3 x^3 + y^3 + 3xy(x + y) General Form
(2x + 1)^3 8x^3 + 12x^2 + 6x + 1 Substitute a=2x, b=1
(100 + 2)^3 100^3 + 2^3 + 3(100)(2)(102) Numerical Application

Practice Questions

Try solving these extra questions to strengthen your grasp on the topic:

  1. Expand (3x + 4y)^3 using the standard identity.
  2. Find the value of 105^3 using the identity (100 + 5)^3.
  3. Factorize: 27a^3 + 64b^3 + 108a^2b + 144ab^2.
  4. If x + 1/x = 3, find the value of x^3 + 1/x^3 using the cubic identity.
  5. Verify the identity for a = 1 and b = -2.