Simplify: (a + b)^3 - (a - b)^3. | Mathematics MCQ | Examoogle

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Simplify: (a + $b)^3$ - (a - $b)^3$ .

$2b^3 + 6a^2b$

$2a^3 + 6ab^2$

$6a^2b + 2b^3$

$6ab^2 + 2a^3$

Correct Answer

📐 MA • Math Algebraic IdentityMathematicsMathematics

Option C

$6a^2b + 2b^3$

Quick Summary:

Memorize standard cube identity differences like $(a+b)^3 - (a-b)^3 = 6a^2b + 2b^3$ to write the answer in seconds.

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📐MAMath SolutionAlgebraic Identity

📋 Given

The expression to simplify is given as (a + $b)^3$ - (a - $b)^3$ .

🔢 Formula Used

(a±b)3=a3±3a2b+3ab2±b3(a \pm b)^3 = a^3 \pm 3a^2b + 3ab^2 \pm b^3(a±b)3=a3±3a2b+3ab2±b3

⚡ Exam Hall Shortcut / Speed Trick

Memorize standard cube identity differences like $(a+b)^3 - (a-b)^3 = 6a^2b + 2b^3$ to write the answer in seconds.

⚠️ Common Student Trap / Pitfall

Failing to distribute the negative sign to all terms inside the expansion of $(a-b)^3$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Expand the first cube

Use the algebraic expansion formula for $(a+b)^3$ : $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ .

(a+b)3=a3+3a2b+3ab2+b3(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3(a+b)3=a3+3a2b+3ab2+b3

Expand the second cube

Use the expansion formula for $(a-b)^3$ : $(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$ .

(a−b)3=a3−3a2b+3ab2−b3(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3(a−b)3=a3−3a2b+3ab2−b3

Subtract and simplify

Subtract the second expression from the first, distributing the negative sign to get $(a+b)^3 - (a-b)^3 = 6a^2b + 2b^3$ .

(a+b)3−(a−b)3=6a2b+2b3(a+b)^3 - (a-b)^3 = 6a^2b + 2b^3(a+b)3−(a−b)3=6a2b+2b3

✅

C is correct because expanding and subtracting both terms results in $6a^2b + 2b^3$ .

Core Concepts Used

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Algebraic Identities Binomial Expansion Simplification

💡 EXAM TIP

Mastering algebraic identities helps solve polynomial division and factorization problems quickly in quantitative aptitude sections.

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