Calculate the expression (3^3-1)(3^3+1)(3^6+1… | GMAT Sprint

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PS · Problem Solving

555-605

Algebra

Calculate the expression $(3^3-1)(3^3+1)(3^6+1)(3^{12}+1)=$

What is the simplified result?

Answer Choices

Correct answer marked below

3^{24} +1

3^{48} -1

3^{24} -1

Correct

3^{96} +1

3^6(3^{12} -1)

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Explanation

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Official Explanation

Official

To simplify the expression

(3^3-1)(3^3+1)(3^6+1)(3^{12}+1)

, we can use the difference of squares and properties of exponents. First, notice that

(3^3-1)(3^3+1) = 3^6 - 1

. Next, we can rewrite

(3^6+1)(3^{12}+1)

using the same principle. The expression

(3^6+1)(3^{12}+1)

can be simplified as follows: [m](3^6 -…

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Comments

SrikanthApr 16, 2025

Greatt

TarekApr 28, 2025

Great!

ananyaApr 20, 2025

thanks!

KhánhFeb 19, 2025

Great question!

RohitMar 12, 2025

thanks!

ShivamAug 9, 2024

Great!

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Calculate the expression (33−1)(33+1)(36+1)(312+1)=(3^3-1)(3^3+1)(3^6+1)(3^{12}+1)=(33−1)(33+1)(36+1)(312+1)= What is the simplified result?