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.