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!

VeidesAug 23

thanks, this one was a nice reminder that difference of squares keeps going as long as the terms line up.

EvanSep 4

wait how did you know which two to pair first? i just started multiplying everything and got lost lol

ZofishanJun 5

I picked A at first because I thought the +1 would stay, but then realized the pattern keeps flipping signs. tricky little trap.

TiffanyJun 18

same, the last factor convinced me it had to be minus

PatJun 10

Is there a faster way to see this without expanding? Felt like I was doing too much work for a 555-605.

VionaJun 6

got C, felt pretty straightforward once you spot the conjugate pairs

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?