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

This Class IX Mathematics quiz focuses on Unit II: Algebra, specifically the verification and application of the algebraic identity (a+b)^2. Test your skills in expanding binomials and factorizing perfect square trinomials as per CBSE Code 041 standards. Complete the 10 questions below, click submit to check your score, and download the detailed answer PDF for your revision.

Understanding the Identity (a + b)^2

In Class 9 Algebra, one of the most fundamental identities is the square of a binomial sum. The identity states that the square of the sum of two terms is equal to the square of the first term, plus twice the product of the two terms, plus the square of the second term.

Formula: (a + b)^2 = a^2 + 2ab + b^2

Geometric Interpretation

Geometrically, this identity represents the area of a large square with side length (a + b). This large square can be divided into two smaller squares with areas a^2 and b^2, and two rectangles, each with area ab. Adding these parts gives the total area: a^2 + 2ab + b^2.

Key Applications

  • Expansion: Converting a factored form like (3x + 4)^2 into its expanded polynomial form.
  • Factorization: Recognizing a trinomial like 4x^2 + 12x + 9 as a perfect square and converting it back to (2x + 3)^2.
  • Numerical Calculation: Calculating squares of numbers like 103^2 by writing them as (100 + 3)^2 to simplify mental math.

Common Mistakes to Avoid

A frequent error students make is distributing the exponent directly to the terms inside the parenthesis, thinking that (a + b)^2 equals a^2 + b^2. This is incorrect because it misses the middle term, 2ab. Always remember to include the “twice the product” term.

Practice Questions

Try solving these additional problems to strengthen your understanding:

  1. Expand: (5x + 1)^2
  2. Find the value of 105^2 using the identity.
  3. Factorize: x^2 + 18x + 81
  4. If a + b = 7 and ab = 10, find the value of a^2 + b^2.
  5. Expand: (ab + c)^2