Multiplying Out Brackets
Multiplying Out Brackets
In this video, we are going to go over how we multiply numbers out of brackets. This is so so important to learn as this comes up A LOT in Algebra.
There are a few levels of difficulty when it comes to brackets – you can have one bracket like \(4x(2x+1) \), two brackets like \((4x+1)(2x+1) \) and you can also have three brackets like:
\((4x+1)(2x+1)(3x+2)\).
Single Bracket
First lets tackle a single bracket. This is graded as 3 or between a D and an E grade.
\(4x(2x+1)\)
All we do here is multiply whatever is inside of the bracket, by the terms on the outside of the bracket.
So in this example, we would first multiply the \(2x\) by the \(4x\) which will give us \(8x^2\), then the \(1\) by \(2x\) which will give us \(2x.\)
So our expression when we multiply out the brackets will be \(8x^2 + 2x\).
Simple enough?
Double Brackets
Now let’s try double brackets. This is graded as 4 or a C.
So we’ll use the example in our introduction of :
\((4x+1)(2x+1)\)
Similar to our single bracket, we first take the first number of our first bracket, and multiply it by both of the numbers in the second bracket.
We take our \(4x\) and multiply it by the \(2x\) and the \(1\) which we know from our single brackets example gives us \(8x^2 + 2x\).
The only difference for double brackets is that we now need to do that same with the second number in our first brackets.
So our \(+1\) needs to be multiplying against the \(2x\) and the \(+1\). After multiplying \(2x+1\) we’ll be left with \(2x+1.\)
Now we just need to ‘collect our terms’. We’ve got \(8x^2 + 2x +2x +1\). So our final answer would be \(8x^2 + 4x + 1.\)
Triple Brackets
Now for the Triple Brackets. Although this is graded as 7, the equivalent to an A, it’s not as hard as it sounds.
You simply multiply 2 of the 3 brackets out as above. Let’s use an example of:
\((4x+1)(2x+1)(3x+2)\).
We’ve already got our answer for \((4x+1)(2x+1)\) in our Double Brackets example so we can re-write the triple brackets as \((8x^2+4x+1)(3x+2)\).
Now we’ve got a ourselves a double bracket. We multiply each of the numbers in the first bracket by each of the numbers in the second bracket.
\(8x^2 \times 3x = 24x^3\)
\(4x \times 3x = 12x^2 1 \times 3x = 3x\)
\(8x^2 \times 2 = 16x^2\)
\(4x \times 2 = 8x\)
\(1 \times 2 = 2\)
So now we’ve got \(24x^3 + 12x^2 + 3x + 16x^2 + 8x + 2\) which looks a little bit ugly. So we need to collect our terms.
This gives us \(24x^3 + 28x^2 + 11x + 2\) which is our answer.
Hopefully, this made sense and if you’ve got any questions, please feel free to put them in the forum area under Multiplying Out Brackets and I’ll get back to you as soon as possible.
You can find some practice question worksheet below to make sure you’re comfortable with Multiplying Out Brackets – give them a go!