\(\left( {1456 + 23} \right) - 1456 = \left( {1456 - 1456} \right) + 23 = 23.\)

\(\left( {116 + 124} \right) + \left( {215 - 116 - 124} \right) = \left( {116 - 116} \right) + \left( {124 - 124} \right) + 215 = 215\)

\(\left( {435 - 167 - 89} \right) - \left( {435 - 89} \right) = \left( {435 - 435} \right) + \left( { - 89 + 89} \right) - 167 = - 167.\)

\[\left( {a + b + c} \right) - \left( {a - b + c} \right) = a + b + c - a + b - c = 2b\]

\[\left( {a + b - c} \right) + \left( {a - b} \right) - \left( {a - b - c} \right) = a + b - c + a - b - a + b + c = a + b\]

\[ - \left( {a - b - c} \right) - \left( { - a + b + c} \right) - \left( {a - b + c} \right) = - a + b + c + a - b - c - a + b - c = - a + b - c\]

\(\left( {a - b + c - d} \right) - \left( {a + b + c + d} \right) = a - b + c - d - a - b - c - d = - 2b - 2d = - 2\left( {b + d} \right)\)

\(\left( { - a + b - c} \right) + \left( {a - b} \right) - \left( {a - b + c} \right) = - a + b - c + a - b - a + b - c = - a + b - 2c\)

\( - \left( {a - b - c} \right) + \left( {b - c + d} \right) - \left( { - a + b + d} \right) = - a + b + c + b - c + d + a - b - d = b.\)

\[x + 8 - y = \left( { - 53} \right) + 8 - 45 = - 45 - 45 = - 90\]

\[x + y + z - y = x + z = \left( { - 53} \right) + \left( { - 15} \right) = - 68\]

\[16 + x - (y + z) - x = 16 - \left[ {45 + \left( { - 15} \right)} \right] = 16 - 30 = - 14\]

Với a = -13, b = 25, c = -30. Ta có

\(a + a + 12 - b = 2a - b + 12 = 2.\left( { - 13} \right) - 25 + 12 = - 39\)

Với a = -13, b = 25, c = -30. Ta có

\(25 + a - \left( {b + c} \right) - a = 25 - b - c = 25 - 25 + 30 = 30.\)

\(382 + 531 - 282 - 331 = \left( {382 - 282} \right) + \left( {531 - 331} \right) = 100 + 200 = 300;\)

)\(7 - 8 + 9 - 10 + 11 - 12 + ... + 2009 - 2010\)

\( = \left( {7 - 8} \right) + \left( {9 - 10} \right) + \left( {11 - 12} \right) + ... + \left( {2009 - 2010} \right)\)

\( = \underbrace {\left( { - 1} \right) + \left( { - 1} \right) + ... + \left( { - 1} \right)}_{gom{\rm{ }}\,1002\,{\rm{ }}so\,hang\, - 1} = - 1002\)

\( - 1 - 2 - 3 - 4 - ... - 2008 - 2009 - 2010\)

\( = - \left( {1 + 2 + 3 + ... + 2008 + 2009 + 2010} \right) = \frac{{\left( {1 + 2010} \right).2010}}{2} = - 2021055\)

\(1 - 3 - 5 + 7 - 9 - 11 + ... + 1000 - 1002 - 2004\)

\[ = \left( {1 - 3 - 5} \right) + \left( {7 - 9 - 11} \right) + ... + \left( {1000 - 1002 - 1004} \right)\]                               \[ = \underbrace {\left( { - 7} \right) + \left( { - 7} \right) + ... + \left( { - 7} \right)}_{gom\,334\,so\,hang\,} = - \left( {\underbrace {7 + 7 + ... + 7}_{gom\,334\,so\,hang}} \right) = - 7\,.\,334 = - 2338.\]