Simplifying Algebraic Expressions - Removing Brackets

Lesson Objective

Learn how to remove brackets in algebraic expressions.

About This Lesson

Algebraic expressions may contain brackets. In order to simplify the expressions, you may need to remove the brackets.

This lesson shows you the basics that you need to know when removing brackets.

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.

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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.

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

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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.

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

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Let' remove the brackets in this term.

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

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Let's put back this term, positive 6a,  back into the expression.

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Now, let's remove the brackets in this term.
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First,  multiply -2 with 4a. This gives -a.

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Then, we multiply -2 with -3b. This gives +6b.

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Let's put these terms back into the expression.

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

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

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One last example, simplify this expression.

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

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

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Knowing this, we now multiply -1with 2x. This gives -2x.

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Now, we multiply -1 with -3. This gives +3. 

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Let's put back these terms  back into the expression.

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Now, let's remove the brackets for 2(x+4).

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Multiply  +2 with x. This gives 2x.

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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.

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

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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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