My Math Forum Bracket expansion problem

 Calculus Calculus Math Forum

 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(3-x-2y)^2 I know easy expansions like (3-2y)^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: 7,618 Thanks: 2608 Math Focus: Mainly analysis and algebra $$2(3-x-2y)^2 = 2(3-x-2y)(3-x-2y)$$ 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(3-x-2y)^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(3-x-2y)}\right) \\ &= 2(9 - 6x -12y +x^2 +4xy +4y^2) \\ &= 18 - 12x -24y +2x^2 +8xy +8y^2 \\ \end{align*} Thanks from pcurran871

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