Albert Teen YOU ARE LEARNING:  Expanding Brackets  # 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.

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What does this equal?  2

What if we add brackets? What does this equal now?  3

So brackets matter for the result!

By the way, notice that when you multiply brackets, you don't need to write the multiplication sign.

$3 \times (4+2)$ is the same as just $3(4+2)$ 1

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. 2

Basically, the $3$ wants to be multiplied by both terms inside the brackets. What is $3 \times 4$?  3

And what is $3\times2$?  4

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. 1

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. 2

To expand the brackets here, you first have to say $2 \times x$. What is that?  3

Then you say $2\times 4$. What is that?  4

Now the brackets are expanded

Now you can simplify the expression. 5

You have $3x$ and another $2x$. How many $x$ is that in total?  6

So you expanded the brackets to simplify this expression

$5x+8$ is a lot easier to read than $3x+2(x+4)$ Expand $5(3+x)$ 1

Recap! You can expand brackets to simplify expressions

For example, $6x+20$ is a lot easier to read than $2x+4(x+5)$ 2

To expand brackets, you need to multiply all the terms inside the brackets by the number outside the brackets

First you say $4 \times x=4x$ Then you say $4\times5=20$ Then you put the two together $4x+20$ 3

Finally, you can see if you can simplify the whole expression

In this case, you have $2x$ and $4x$ which you can combine to $6x$ Expand $6(x+2)$ Expand $(x+6)8$ Now, what is $2(x-4)$ when you expand the brackets? Let's try this one $x(3x+6)$.

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What happens when the number outside the bracket is also a variable?

We apply the same principle.

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First we multiply $x\times 3x$. What does this give us? 3

Next we multiply the second term in the bracket. What is $x\times 6$? 4

We have $x\times 3x=3x^2$ and $x\times 6=6x$.

Putting these together we have $3x^2+6x$.

Expand $(x-2)4x$ Expand and simplify $(2+3x)5-4x$ Expand and simplify $x(8+3x)-2x$ 1

Summary! You can expand brackets to simplify expressions

For example, $6x+3x^2$ is easier to read than $x(8+3x)-2x$ 2

So how do you expand brackets?

You multiply both terms inside the bracket by the number outside the bracket. 3

The number might follow the brackets rather than stand before them

Don't be confused by that. 4

If you multiply a positive and a negative, then remember to keep the minus!

For example, $2 \times -4$ is $-8$, so this becomes $2x-8$, not $2x+8$ 5

If you multiply $x\times x$ it becomes $x^2$

So if you multiply $x \times 3x$ as in this example, it becomes $3x^2$ 