The value of 27 3 - 22 3 is: | Mathematics MCQ | Examoogle

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The value of 27 3 - 22 3 is:

$9035$

$8823$

$8923$

$8888$

Correct Answer

📐 MA • Math Algebraic IdentityMathematicsAlgebra

Option A

$9035$

Quick Summary:

Check the unit digit: $27^3$ ends in 3 ( $7^3 = 343$ ) and $22^3$ ends in 8 ( $2^3 = 8$ ). The difference must end in $13 - 8 = 5$ . Only Option A ends in 5.

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📐MAMath SolutionAlgebraic Identity

📋 Given

We are given two numbers, 27 and 22, and we need to find the difference between their cubes: 27³ - 22³.

🔢 Formula Used

a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2)a3−b3=(a−b)(a2+ab+b2)

⚡ Exam Hall Shortcut / Speed Trick

Check the unit digit: $27^3$ ends in 3 ( $7^3 = 343$ ) and $22^3$ ends in 8 ( $2^3 = 8$ ). The difference must end in $13 - 8 = 5$ . Only Option A ends in 5.

⚠️ Common Student Trap / Pitfall

Students often miscalculate large cubes (272727 = 19683 and 222222 = 10648) leading to simple arithmetic errors under pressure.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify values and formula

Set $a = 27$ and $b = 22$ . Use the difference of cubes identity to simplify the calculation.

a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2)a3−b3=(a−b)(a2+ab+b2)

Substitute the values

Substitute $a=27$ and $b=22$ into the formula. First, calculate the difference: $27 - 22 = 5$ .

273−223=(27−22)(272+27×22+222)27^3 - 22^3 = (27 - 22)(27^2 + 27 \times 22 + 22^2)273−223=(27−22)(272+27×22+222)

Calculate the squares and product

Calculate $27^2 = 729$ , $22^2 = 484$ , and $27 \times 22 = 594$ . Then sum these values: $729 + 594 + 484 = 1807$ .

1807×5=90351807 \times 5 = 90351807×5=9035

✅

A is correct because the application of the identity $27^3 - 22^3 = (27 - 22)(27^2 + 27 \times 22 + 22^2)$ yields $5 \times 1807 = 9035$ .

Core Concepts Used

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Algebraic Identities Cube Difference Arithmetic Simplification

💡 EXAM TIP

Understanding the algebraic expansion of cubes is essential for high-speed calculation in Quantitative Aptitude, often appearing in simplification questions in SSC and banking exams.

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