Multiplying out brackets is expanding an expression.
For example: expand 3a(4a - 3b + 6). Set out the terms within the brackets as a list, deal with them individually, then add them together:
4a x 3a = 12a2
-3b x 3a = -9ab
6 x 3a = 18a
Note that every term in the bracket is multiplied by the term outside the bracket, and that negative signs are taken into account. Put the answer together:
3a(4a - 3b + 6) = 12a2 - 9ab + 18a
1. Expand and simplify 3(m + 2) + 4m.
Answer: 7m + 6
Expand the bracket:
m x 3 = 3m
2 x 3 = 6
Put it all together. Include the 4m that was outside the bracket:
3m + 6 + 4m = 7m + 6
2. Expand and simplify: 6 - a(a - 2).
Answer: -a2 + 2a + 6
Expand the brackets, taking very careful note of the negative signs:
a x -a = -a2
-2 x -a = 2a
Putting it all together, with the leading 6:
-a2 + 2a + 6
It is normal to put a list of terms in descending order of their powers.