Simplifying Algebraic Expressions - Removing Brackets

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Lesson Objective

Learn how to remove brackets when simplifying algebraic expressions...

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About This Lesson

Algebraic expressions can contain brackets. In order to simplify these kind of expressions, you may need to remove the brackets.

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

Removing brackets

Study Tips

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Tip #1

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

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Tip #2

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

Now, watch the following math video to know more.

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Math Video Transcript

Simplifying Algebraic Expressions - Removing Brackets

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 in simplifying algebraic expressions 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.

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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.

00:01:55.170
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.

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.

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One last example on simplifying algebraic expressions.

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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.

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.

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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).

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 in simplifying algebraic expressions. Try out the practice questions to test your understanding.

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