# Question #6d036

May 30, 2016

a) $5 x + 12$

#### Explanation:

Expanding is the opposite of factoring. When you have a number in front of parentheses, it means that number (called factor) is multiplying each number inside the parentheses. Therefore, for letter a, we have:

$3 \left(x + 2\right) + 2 \left(x + 3\right) = \left(3 \cdot 1 x\right) + \left(3 \cdot 2\right) + \left(2 \cdot 1 x\right) + \left(2 \cdot 3\right)$.

Solving these multiplications, the output is:

$3 x + 6 + 2 x + 6$.

The next part is simplifying the operation. We can sum and subtract like thers, that is, sum numbers without letters with other numbers without letters, and numbers with x with other numbers with x. I have rewritten the order to make the visualization easier:

$3 x + 2 x + 6 + 6 = 5 x + 12$

Now try doing the next exercises and watch out for the signs. The calculation for $x$,$n$, $t$ and $w$ is the same, just don't mix the letters.