Simplifying Algebraic Expressions - Removing Brackets
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.
Remember to multiply all the terms in the brackets with the term outside the brackets.
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.
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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.
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Multiple Choice Questions (MCQ)
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