If x^2 + 4xy + 4y^2 = 16, then (x + 2y)^2 = | GMAT Sprint

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PS · Problem Solving

sub-505

Algebra

If $x^2 + 4xy + 4y^2 = 16$ , then $(x + 2y)^2 =$

Answer Choices

Correct answer marked below

4

16

Correct

8

32

64

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Explanation

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Official Explanation

Official

To solve for

(x + 2y)^2

, we start with the given equation

x^2 + 4xy + 4y^2 = 16

. Notice that the left side can be factored as…

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Comments

ArpanJan 7, 2025

Amazing

SubhamJan 25, 2025

thankss

AishwaryaFeb 11, 2025

Thank you very much!

ArpitApr 11, 2025

Great explanation

ashrithFeb 10, 2025

thanks for taking time to upload it!

PriyadarshiniMar 25, 2025

Thankss

ClifordApr 28

easy one, just factor the left side

SamiyahMay 7

yeah once you see x^2 + 4xy + 4y^2 as a perfect square it's basically free

JohnJul 6

wait is it really just 16? feels too simple for a GMAT question lol

VaivaJun 27

thanks!

AdaJun 30

np, these perfect square trinomials show up a lot so good to lock in the pattern

AvilashJul 15

I almost picked 4 because I took the square root, good thing I re-read. classic trap

LowiJul 23

same trap lol, you're not alone

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.

If x2+4xy+4y2=16x^2 + 4xy + 4y^2 = 16x2+4xy+4y2=16, then (x+2y)2=(x + 2y)^2 =(x+2y)2=