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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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