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May 15th, 2014, 06:00 PM   #1
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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.

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May 15th, 2014, 06:22 PM   #2
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$$2(3-x-2y)^2 = 2(3-x-2y)(3-x-2y)$$
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*}
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