YOU ARE LEARNING:
Expanding Brackets
Expanding Brackets
Expanding brackets is an important step for manipulating expressions, and involves multiplying the terms inside a bracket by those outside of a bracket.
What does this equal?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/EqYCtRL3SuCQYcgSS23n.png)
What if we add brackets? What does this equal now?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/QntqWubyS9aFvrKr2WsB.png)
So brackets matter for the result!
By the way, notice that when you multiply brackets, you don't need to write the multiplication sign.
3×(4+2) is the same as just 3(4+2)
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/JYhkMJL9SfuOq1rJeVwK.png)
Now, you could also work out this problem in a different way
You could also change the expression so that the brackets disappear. That is called expanding the brackets.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/JYhkMJL9SfuOq1rJeVwK.png)
Basically, the 3 wants to be multiplied by both terms inside the brackets. What is 3×4?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/tszuCEJlSTW0pGz3j0tk.png)
And what is 3×2?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/rn1ysNKTcaSQtCvoOtz0.png)
Now, you have 12+6
So 12+6 is the same as 3(4+2), but you have expanded the brackets - you have made them disappear.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/TjzOQLpoRQGPdpeMBVjO.png)
But why would you want to expand brackets?
It can help you simplify expressions to make them easier to read. This example shows you how.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Y2fQyuctSxeuJcFNk6mL.png)
To expand the brackets here, you first have to say 2×x. What is that?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/4dwxWNWQqawvuqiAWB72.png)
Then you say 2×4. What is that?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/yd54X3HJQgmLT3EWN0Cu.png)
Now the brackets are expanded
Now you can simplify the expression.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Xly3wyqRwCFzJ8hF75fA.png)
You have 3x and another 2x. How many x is that in total?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Xly3wyqRwCFzJ8hF75fA.png)
So you expanded the brackets to simplify this expression
5x+8 is a lot easier to read than 3x+2(x+4)
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/dYRSrvkdT367pakaWczj.png)
Expand 5(3+x)
Recap! You can expand brackets to simplify expressions
For example, 6x+20 is a lot easier to read than 2x+4(x+5)
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/csshTbbQiabdT7V7Ve3f.png)
To expand brackets, you need to multiply all the terms inside the brackets by the number outside the brackets
First you say 4×x=4x Then you say 4×5=20 Then you put the two together 4x+20
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/csshTbbQiabdT7V7Ve3f.png)
Finally, you can see if you can simplify the whole expression
In this case, you have 2x and 4x which you can combine to 6x
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/csshTbbQiabdT7V7Ve3f.png)
Expand 6(x+2)
Expand (x+6)8
Now, what is 2(x−4) when you expand the brackets?
Let's try this one x(3x+6).
What happens when the number outside the bracket is also a variable?
We apply the same principle.
First we multiply x×3x. What does this give us?
Next we multiply the second term in the bracket. What is x×6?
We have x×3x=3x2 and x×6=6x.
Putting these together we have 3x2+6x.
Expand (x−2)4x
Expand and simplify (2+3x)5−4x
Expand and simplify x(8+3x)−2x
Summary! You can expand brackets to simplify expressions
For example, 6x+3x2 is easier to read than x(8+3x)−2x
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/j8zMhyoQ52D2CYWSoQ0A.png)
So how do you expand brackets?
You multiply both terms inside the bracket by the number outside the bracket.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/j8zMhyoQ52D2CYWSoQ0A.png)
The number might follow the brackets rather than stand before them
Don't be confused by that.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/Lu3ChzGIRTicTl1C9wWf.png)
If you multiply a positive and a negative, then remember to keep the minus!
For example, 2×−4 is −8, so this becomes 2x−8, not 2x+8
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/DHulElysTnWCAtBWGkjZ.png)
If you multiply x×x it becomes x2
So if you multiply x×3x as in this example, it becomes 3x2
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/j8zMhyoQ52D2CYWSoQ0A.png)