Select the term which is not an identity. | Mathematics MCQ

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MathematicsPrevious Year Paper 2024

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Select the term which is not an identity.

$(a + b)^2 = a^2 + b^2$

$(a + b)^2 = a^2 + b^2 + 2ab$

$(a + 1)(a + 2) = a^2 + 3a + 2$

$(a - b)^2 = a^2 + b^2 - 2ab$

Correct Answer

📐 MA • Math Algebraic ExpansionMathematicsPrevious Year Paper 2024

Option A

$(a + b)^2 = a^2 + b^2$

Quick Summary:

An algebraic identity must hold true for all values of the variables. Test small integers like $a=1, b=2$ . If the LHS does not equal the RHS, it is not an identity.

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📐MAMath SolutionAlgebraic Expansion

📋 Given

Four algebraic expressions are provided as options, and the goal is to identify which one is NOT an algebraic identity.

🔢 Formula Used

(a+b)2=a2+b2+2ab(a+b)^2 = a^2+b^2+2ab(a+b)2=a2+b2+2ab

⚡ Exam Hall Shortcut / Speed Trick

An algebraic identity must hold true for all values of the variables. Test small integers like $a=1, b=2$ . If the LHS does not equal the RHS, it is not an identity.

⚠️ Common Student Trap / Pitfall

Many students mistake $(a+b)^2 = a^2+b^2$ for an identity, forgetting the middle term $2ab$ .

🔢 Step-by-Step Solution

Check Option A

Evaluate the expression $(a+b)^2 = a^2+b^2$ . If $a=1, b=1$ , then $(1+1)^2 = 2^2 = 4$ , while $1^2+1^2 = 2$ . Since $4 \neq 2$ , this is not an identity.

(a+b)2≠a2+b2(a+b)^2 \neq a^2+b^2(a+b)2=a2+b2

Check Option B

The expansion of $(a+b)^2$ is $(a+b)(a+b) = a^2+ab+ab+b^2 = a^2+b^2+2ab$ . This is a standard identity.

(a+b)2=a2+b2+2ab(a+b)^2 = a^2+b^2+2ab(a+b)2=a2+b2+2ab

Check Option C

Expanding $(a+1)(a+2)$ : $a(a+2) + 1(a+2) = a^2+2a+a+2 = a^2+3a+2$ . This is a correct algebraic expansion/identity.

(a+1)(a+2)=a2+3a+2(a+1)(a+2) = a^2+3a+2(a+1)(a+2)=a2+3a+2

Check Option D

The expansion of $(a-b)^2$ is $(a-b)(a-b) = a^2-ab-ab+b^2 = a^2+b^2-2ab$ . This is a standard identity.

(a−b)2=a2+b2−2ab(a-b)^2 = a^2+b^2-2ab(a−b)2=a2+b2−2ab

✅

A is correct because the expression $(a+b)^2 = a^2+b^2$ is an incorrect mathematical statement and fails to satisfy the definition of an algebraic identity.

Core Concepts Used

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Algebraic Identity Binomial Expansion Mathematical Equality

💡 EXAM TIP

This concept is fundamental for simplifying polynomials in higher algebra and factorizing quadratic equations.

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