a (a+b+c) + (a-b+c) - (b+c-a) - (a-b-c)
=a+b+c+a-b+c-b-c+a-a+b+c
= (a+a+a-a) + (b-b+b-b) + (c+c+c-c)
= a x 2 + 0 + c x 2
= 2 x (a + c)
\(\left(a+b-c\right)+\left(a-b+c\right)-\left(a-b-c\right)\)
\(=a+b-c+a-b+c-a+b+c\)
\(=\left(a+a-a\right)+\left(b-b+b\right)+\left(c-c+c\right)\)
\(=a+b+c\)
\(x-\left(+5\right)-\left[\left(x+11\right)-\left(x-11\right)\right]\)
\(=x-5-\left[x+11-x+11\right]\)
\(=x-5-\left[x-x+11+11\right]\)
\(=x-5-22\)
\(=x-27\)
\(a-\left\{\left(a-5\right)-\left[\left(a+9\right)-\left(-a+1\right)\right]\right\}\)
\(=a-\left\{a-5-\left[a+9+a-1\right]\right\}\)
\(=a-\left\{a-5-\left[a+a+9-1\right]\right\}\)
\(=a-\left\{a-5-\left[2a+8\right]\right\}\)
\(=a-\left\{a-5-2a-8\right\}\)
\(=a-a+5+2a+8\)
\(=2a+13=2\left(a+6\right)+1\)
