BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Factoring

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 31
Joined: Sun Jul 31, 2011 10:55 amFollowed by: 1 member
by HeyArnold » Sun Aug 07, 2011 8:04 am
Given that [A, B] = A^2 + B^2 + 2AB, what is A + B if [A, B] = 9?

[spoiler]OA: {3, -3} this is from Manhattan guide 3, the answer alludes to factoring but doesn't show it...

Thanks!
[/spoiler]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 111
Joined: Tue Dec 30, 2008 1:25 pm
Location: USA
Thanked: 28 times
GMAT Score:770

by goalevan » Sun Aug 07, 2011 2:11 pm
A^2 + 2AB + B^2 is the sum of squares formula, and equals (A + B)^2:

A^2 + 2AB + B^2
A^2 + AB + AB + B^2
A(A + B) + B(A + B)
(A + B)(A + B)
(A + B)^2

Therefore [A, B] = (A + B)^2

[A, B] = 9
(A + B)^2 = 9
A + B = -3 or 3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 509
Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members
Location: Irvine, CA
Thanked: 199 times
GMAT Score:750

by tpr-becky » Sun Aug 07, 2011 11:19 pm
This problem is better understood if you move the formula around to create A^2 + 2AB + B^2 - this is a common quadratic that is factored out to (A + B)(A + B).

If 9 = A^2 + B^2 + 2AB, then 9 = (A + B)(A + B) thus sqrt9 = A + B which means that A+B = 3 or -3
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1