Simplifying Algebraic Expressions - Removing Brackets Lesson Objective

Learn how to remove brackets when simplifying algebraic expressions... 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. 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 the terms together in order to remove the brackets in the expression.

Now, watch the following math video to know more.

Math Video Click play to watch Math Video Transcript

Simplifying Algebraic Expressions - Removing Brackets

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Algebraic expressions may contain brackets.

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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 in simplifying algebraic expressions to understand this better.

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

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When you add all the 2x, you get 6x.

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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.

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

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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.

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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.

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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 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.

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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.

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

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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.

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

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That's all for this lesson in simplifying algebraic expressions. Try out the practice questions to test your understanding.

Practice Questions & More Multiple Choice Questions (MCQ)

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