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Study Guide : Expanding And Factorising

Learner Guide

 

Maths

Algebra

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Expanding and Factorising

L. O to be able to expand brackets and find common factors

in algebraic expressions


Expanding

When you expand brackets you are multiplying all the terms so that there are

no longer brackets present. The reverse of this is factorising.

 

Example 1

Expand 6 ( x + 3 ) …

Multiply 6 by +3 to get +18

6  ( x + 3 )

Multiply 6 by x first to get 6x = 6x + 18.

 

Step 1: Highlight the different terms inside the brackets.

Step 2: Multiply the outside constant by each term separately.

Step 3: Rewrite including both multiplied terms.

 

Example 2

 

Expand 5 ( x – 8 ) …

Multiply 5 by -8 to get -40

5  ( x – 8 )

Multiply 5 by x first to get 5x = 5x – 40

 

Step 1: Highlight the different terms inside the brackets.

Step 2: Multiply the outside constant by each term separately. In this case

               be careful make sure you highlight -8 and not 8 by itself.

Step 3: Rewrite including both multiplied terms.

 

Example 3

 

Expand 3y ( y2 – 4y + 8 ) …

Multiply 3y by -4y to get -12y2

Multiply 3y by y2 to get 3y3

3y  ( y2 – 4y + 8 )

Multiply 3y by +8 to get +24y = 3y3 – 12y2 + 24y

 

Step 1: Highlight the different terms inside the brackets. Here there are

               more terms but it is exactly the same.

Step 2: Multiply the outside constant by each term separately. In this case

               be careful make sure you remember your index laws when

               multiplying 3y by y2.

Step 3: Rewrite including all multiplied terms.


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Related Topics


Expressions-and-formulae                                           Index-notation

Solving-linear-equations                                                Factorising

 

 



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