#spanend &spanadd; \begin{array}{l}&spanend; &spanadd; \left| \begin{array}{ccc} a&b&c \\ c&a&b \\ b&c&a \end{array} \right|&spanend; &spanadd; = \left| \begin{array}{ccc} a+b+c&b&c \\ c+a+b&a&b \\ b+c+a&c&a \end{array} \right|&spanend; &spanadd; \\\\ = (a+b+c) \left| \begin{array}{ccc} 1&b&c \\ 1&a&b \\ 1&c&a \end{array} \right|&spanend; &spanadd; \\\\ = (a+b+c) \left| \begin{array}{ccc} 1&b&c \\ 0&a-b&b-c \\ 0&c-b&a-c \end{array} \right|&spanend; &spanadd; \\\\ = (a+b+c) \left| \begin{array}{cc} a-b&b-c \\ c-b&a-c \end{array} \right|&spanend; &spanadd; \\\\ = (a+b+c)\big((a-b)(a-c) - (b-c)(c-b)\big)&spanend; &spanadd; \\\\ = (a+b+c)(a^2 - ab - ac + bc + b^2 - 2bc + c^2)&spanend; &spanadd; \\\\ = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca)&spanend; &spanadd; \end{array}&spanend; #spanadd /home/limg/www/LimgMath/eq! You can't use `macro parameter character #' in math mode.
\displaystyle \mathstrut ##
spanend &spanadd; \begin {array}{l}&s...
l.17 \end{align*}
#spanend &spanadd; \begin{array}{l}&spanend; &spanadd; \left| \begin{array}{ccc} a&b&c \\ c&a&b \\ b&c&a \end{array} \right|&spanend; &spanadd; = \left| \begin{array}{ccc} a+b+c&b&c \\ c+a+b&a&b \\ b+c+a&c&a \end{array} \right|&spanend; &spanadd; = \left| \begin{array}{ccc} a+b+c&b&c \\ 0&a-b&b-c \\ 0&c-b&a-c \end{array} \right|&spanend; &spanadd; \\\\ = (a+b+c) \left| \begin{array}{cc} a-b&b-c \\ c-b&a-c \end{array} \right|&spanend; &spanadd; \\\\ = (a+b+c)\big((a-b)(a-c) + (b-c)^2 \big)&spanend; &spanadd; \\\\ = (a+b+c)(a^2 - ab - ac + bc - 2bc + b^2 + c^2)&spanend; &spanadd; \\\\ = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca)&spanend; &spanadd; \end{array}&spanend; #spanadd /home/limg/www/LimgMath/eq! You can't use `macro parameter character #' in math mode.
\displaystyle \mathstrut ##
spanend &spanadd; \begin {array}{l}&s...
l.17 \end{align*}
&spandel; \left| \begin{array}{ccc} a&b&c \\ c&a&b \\ b&c&a \end{array} \right|&spanend; &spandel; = \left| \begin{array}{ccc} a+b+c&b&c \\ c+a+b&a&b \\ b+c+a&c&a \end{array} \right|&spanend; &spandel; = (a+b+c) \left| \begin{array}{ccc} 1&b&c \\ 1&a&b \\ 1&c&a \end{array} \right|&spanend; &spandel; = (a+b+c) \left| \begin{array}{ccc} 1&b&c \\ 0&a-b&b-c \\ 0&c-b&a-c \end{array} \right|&spanend; &spandel; = (a+b+c) \left| \begin{array}{cc} a-b&b-c \\ c-b&a-c \end{array} \right|&spanend; &spandel; = (a+b+c)[(a-b)(a−c) - (b-c)(c-b)]&spanend; &spandel; = (a+b+c)[a^2 − ab - ac + bc + b^2 - 2bc + c^2]&spanend; &spandel; = (a+b+c)[a^2 + b^2 + c^2 − ab - bc - ca]&spanend; &spanadd; \begin{array}{l}&spanend; &spanadd; \left| \begin{array}{ccc} a&b&c \\ c&a&b \\ b&c&a \end{array} \right|&spanend; &spanadd; = \left| \begin{array}{ccc} a+b+c&b&c \\ c+a+b&a&b \\ b+c+a&c&a \end{array} \right|&spanend; &spanadd; \\\\ = (a+b+c) \left| \begin{array}{ccc} 1&b&c \\ 1&a&b \\ 1&c&a \end{array} \right|&spanend; &spanadd; = (a+b+c) \arrs{1 \\ 1 \\ 1}\sx \left( \arrs{b \\ c \\ a} \vx \arrs{c \\ a \\ b} \right)&spanend; &spanadd; \\\\ = (a+b+c) (a^2 + b^2 + c^2 - ab - bc - ca)&spanend; &spanadd; \end{array}&spanend; /home/limg/www/LimgMath/eq! Extra alignment tab has been changed to \cr.
\endtemplate
l.17 \end{align*}
#spanend &spanadd; \begin{array}{l}&spanend; &spanadd; \left| \begin{array}{ccc} a&b&c \\ c&a&b \\ b&c&a \end{array} \right|&spanend; &spanadd; = (a+b+c) \arrs{1 \\ 1 \\ 1}\sx \left( \arrs{b \\ c \\ a} \vx \arrs{c \\ a \\ b} \right)&spanend; &spanadd; \end{array}&spanend; #spanadd /home/limg/www/LimgMath/eq! You can't use `macro parameter character #' in math mode.
\displaystyle \mathstrut ##
spanend &spanadd; \begin {array}{l}&s...
l.17 \end{align*}
#spanend &spanadd; \begin{array}{l}&spanend; &spanadd; \left| \begin{array}{ccc} a&b&c \\ c&a&b \\ b&c&a \end{array} \right|&spanend; &spanadd; = \arrs{a \\ b \\ c} \vx \arrs{c \\ a \\ b} \sx \arrs{1 \\ 1 \\ 1} \cdot \,(a+b+c)&spanend; &spanadd; \end{array}&spanend; #spanadd /home/limg/www/LimgMath/eq! You can't use `macro parameter character #' in math mode.
\displaystyle \mathstrut ##
spanend &spanadd; \begin {array}{l}&s...
l.17 \end{align*}
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