# Question #dfc9b

Nov 2, 2016

This isn't the place to get answers for your homework, so I won't give them to you. But I will help you understand how to answer these questions yourself.

#### Explanation:

The only concept that needs addressing in this answer is how to expand brackets.

With addition, brackets can be removed with not problem. So, $a + \left(b + c\right) = a + b + c$ and $a + \left(b - c\right) = a + b - c$.

With subtraction, we have to be a bit more careful. When expanding a bracket with a minus sign before it, we have to remember the sign of each term changes (because we multiply it by $- 1$). So, $a - \left(b + c\right) = a - b - c$ and $a - \left(b - c\right) = a - b + c$.

The final thing to mention is that when bringing like terms together, we use the sign that comes before the terms and not the operation. So, $\left(2 a + 1\right) - \left(a - 5\right) = 2 a + 1 - a + 5 = a + 6$ and $\left(2 a + 1\right) + \left(5 - a\right) = a + 6$. Although the operation in the second example was addition, we subtract as the sign before $a$ was $-$. This is an area where students can easily make mistakes..