May 15th, 2014, 06:00 PM  #1 
Newbie Joined: May 2014 From: Leeds Posts: 3 Thanks: 0  Bracket expansion problem
I hope this is in the right forum... How do I expand this? 2(3x2y)^2 I know easy expansions like (32y)^2 but I don't know how to do this. Any help always appreciated. Thanks Paddy 
May 15th, 2014, 06:22 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,396 Thanks: 2477 Math Focus: Mainly analysis and algebra 
$$2(3x2y)^2 = 2(3x2y)(3x2y)$$ And now each term in the first bracket multiplies each term in the second bracket (just as if there were only two terms in each bracket). \begin{align*} 2(3x2y)^2 &= 2\left(\underbrace{(9  3x 6y)}_{3(3  x 2y)} + \underbrace{(3x + x^2 + 2xy)}_{x(3  x  2y)} + \underbrace{(6y + 2xy + 4y^2)}_{2y(3x2y)}\right) \\ &= 2(9  6x 12y +x^2 +4xy +4y^2) \\ &= 18  12x 24y +2x^2 +8xy +8y^2 \\ \end{align*} 

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