Simplifying Algebraic Expressions - Removing Brackets

Lesson Objective

Learn how to remove brackets in algebraic expressions.

Study Tips

Tip #1

Remember to multiply all the terms in the brackets with the term outside the brackets.

Tip #2

It is important understand why you are able to multiply terms together in order to remove the brackets in an expression.

Now, watch the following math video to know more.

Math Video

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Math Video Transcript

00:00:02.060
Algebraic expressions may contain brackets.

00:00:06.020
You can remove these brackets by multiplying all the terms in the brackets with the term outside the bracket.

00:00:13.060
Now, let's look at some examples to understand this better.

00:00:19.090
Take 3(2x) as an example. This expression is equals to  2x + 2x + 2x.

00:00:31.090
When you add all the 2x, you get 6x.

00:00:37.190
Now, notice that, if you multiply 3 with 2, you will also get 6.  Therefore, you can get the same answer 6x, by multiplying 3 with 2x.  

00:00:50.210
Let's take another example, 2(x+1).  

00:00:55.220
This expression is equals to x+1 plus x+1.

00:01:05.010
If you simplify this expression, you get x + x = 2x , and 1, plus 1, equals to 2.

00:01:15.180
Now, notice this, you can also get 2x by just multiplying 2 with x. 

00:01:22.240
Similarly, you also can get 2, by just multiplying 2 with 1.

00:01:30.120
Alright, let's apply what you have learn here by simplifying this expression.

00:01:36.210
Let' remove the brackets in this term.

00:01:41.210
To remove the brackets, multiply 2 with 3a. This gives positive 6a. 

00:01:50.010
Let's put back this term, positive 6a,  back into the expression.

00:01:55.170
Now, let's remove the brackets in this term.
00:02:00.210
First,  multiply -2 with 4a. This gives -a.

00:02:07.100
Then, we multiply -2 with -3b. This gives +6b.

00:02:14.020
Let's put these terms back into the expression.

00:02:18.240
Now, notice that you can simplify the like terms +6a  and – 8a. Adding them up gives -2a.

00:02:32.160
The expression is now -2a + 6b. Since there is no more like terms, this is the simplest expression you can get. 

00:02:43.030
One last example, simplify this expression.

00:02:48160
Let's remove the brackets in the term, -(2x -3).

00:02:56.010
Notice this 'negative sign' ,what does it means? This negative sign is actually the the same as -1. 

00:03:06.040
Knowing this, we now multiply -1with 2x. This gives -2x.

00:03:14.110
Now, we multiply -1 with -3. This gives +3. 

00:03:21.140
Let's put back these terms  back into the expression.

00:03:25:13
Now, let's remove the brackets for 2(x+4).

00:03:31.180
Multiply  +2 with x. This gives 2x.

00:03:37.060
Now, multiply +2 with +4. This gives +8.

00:03:44.140
Let's put back these terms  back into the expression. 

00:03:48.220
Now, notice that there are like terms in this expression. Let's group the like terms  together.

00:03:55.070
To simplify this expression, add  +2x with  -2x. These terms cancels off each other.  So, you don't have to write anything.

00:04:07.010
Now, add +3 with  +8. This gives  +11.

00:04:13.150
Since there is no more like terms, this is the simplest expression you can get.

00:04:19.040
That's all for this lesson. Try out the practice questions to test your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on simplifying algebraic expressions - removing brackets or pick your choice of question below.

Question 1 on removing brackets
Question 2 on removing brackets and simplifying

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