Expanding brackets means removing brackets by multiplying everything inside of the bracket by what is just outside of the bracket.
Let's have a look at a few examples to see this in action.
e.g. Expand 3(4x − 2).
We will multiply 3 by 4x and 3 by −2.
3 × 4x = 12x
3 × −2 = −6
Now we put these elements back together to get our final answer:
12x − 6
e.g. Expand −5(7 − 5b).
We will follow the same method, but we need to be careful with the negative signs here.
−5 × 7 = −35
−5 × − 5b = 25b (positive!)
So our answer is:
−35 + 25b
When we multiply a negative by a positive number, our answer is negative.
When we multiply two negative numbers, our answer will be positive.
In this activity, we will expand one set of brackets in calculations and problems, expressing our answers in their simplest forms.