Identity Verification: (a−b)^2 MCQs Quiz | Class 9

This Class IX Mathematics (Code 041) quiz focuses on Unit II: Algebra. It covers the topic of Identity Verification: (a-b)^2, testing your ability to verify and apply the identity for expansion and factorization. Solve these questions, submit your answers to check your score, and download the solution PDF for revision.

Understanding the Algebraic Identity (a-b)^2

In Class 9 Algebra, one of the fundamental identities used for expansion and factorization is the square of a binomial difference. This identity helps in simplifying algebraic expressions, solving equations, and calculating squares of numbers close to a base value efficiently.

The Identity Formula

The standard form of the identity is:

(a – b)^2 = a^2 – 2ab + b^2

Where ‘a’ and ‘b’ can be any variables, numbers, or expressions. This formula states that the square of the difference of two terms is equal to the square of the first term, minus twice the product of the two terms, plus the square of the second term.

Verification

We can verify this algebraically by expanding the product:

  • (a – b)^2 = (a – b)(a – b)
  • = a(a – b) – b(a – b)
  • = a^2 – ab – ab + b^2
  • = a^2 – 2ab + b^2

Applications of the Identity

Type Example Result
Expansion (x – 4)^2 x^2 – 8x + 16
Factorization 9y^2 – 6y + 1 (3y – 1)^2
Numerical (98)^2 = (100 – 2)^2 10000 – 400 + 4 = 9604

Key Points for Exams

  • Always identify ‘a’ and ‘b’ correctly before applying the formula.
  • Remember the middle term is negative: -2ab.
  • If the expression is (-a – b)^2, it is equivalent to (a + b)^2 because the negative sign factors out and squares to positive.
  • Perfect square trinomials of the form A^2 – 2AB + B^2 can always be factorized into (A – B)^2.

Extra Practice Questions

  1. Expand (2x – 5y)^2.
  2. Evaluate 99^2 using the identity.
  3. Factorize x^2 – 18x + 81.
  4. If a – b = 7 and ab = 9, find a^2 + b^2.
  5. Expand (p – 1/p)^2.