YOU ARE LEARNING:
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?
What if we add brackets? What does this equal now?
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)
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.
Basically, the 3 wants to be multiplied by both terms inside the brackets. What is 3×4?
And what is 3×2?
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.
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.
To expand the brackets here, you first have to say 2×x. What is that?
Then you say 2×4. What is that?
Now the brackets are expanded
Now you can simplify the expression.
You have 3x and another 2x. How many x is that in total?
So you expanded the brackets to simplify this expression
5x+8 is a lot easier to read than 3x+2(x+4)
Recap! You can expand brackets to simplify expressions
For example, 6x+20 is a lot easier to read than 2x+4(x+5)
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
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
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 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
So how do you expand brackets?
You multiply both terms inside the bracket by the number outside the bracket.
The number might follow the brackets rather than stand before them
Don't be confused by that.
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
If you multiply x×x it becomes x2
So if you multiply x×3x as in this example, it becomes 3x2