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**Multiplying Out Single Brackets.**

5 X ( 2X + & ) = 10 X ………

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**What Does Multiplying Out A Bracket Mean ?**

Consider this rectangle broken into two areas as shown: 6 A1 A2 We are going to work out the area of this rectangle : x 2 Area = length breadth 6x + 12 A1 = 6 x = 6x Total Area = A2 = 6 2 = 12

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**6 ( x + 2 ) = 6x + 12 Now consider the expression below: Golden Rule:**

Everything inside the bracket must be multiplied by the Number or term outside the bracket. 6 ( x + 2 ) = 6x + 12 The same as the area of the rectangle. Now multiply out the following brackets: (1) 4 ( x + 6 ) (2) 7 ( 2 x + 5 ) (3) 5 ( 8x + 9 ) = 4x + 24 = 14x +35 = 40x + 45

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**What Goes In The Box 1? (1) 6 ( x + 3 ) = 6x + 18 (2) 3 ( 2x + 5 ) =**

Multiply out the brackets below : (1) 6 ( x + 3 ) = 6x + 18 (2) 3 ( 2x + 5 ) = 6x + 15 (3) 4 ( 6x + 7 ) = 24x + 28 (4) 9 ( 3x + 9 ) = 27x + 81 (5) 2 ( 3x + 4 ) = 6x + 8 (6) 8 ( 5x + 7 ) = 40x + 56

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Some Algebra Revision. You should know the answer to the following questions: Multiply out : Calculate : (1) 2y 5 y = 10y 2 (1) 3 - 4 = -12 (2) 3w 4 w = 12w 2 (2) 6 - 7 = - 42 (3) 6r 7r = 42r 2 (3) - 3 8 = - 24 (4) 4f 3f = 12f 2 (4) 7 - 6 = - 42 (5) 9h 8h = 72h 2 (5) - 8 2 = - 16

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**Harder Single Brackets.**

Multiply out the brackets below: (1) 3t ( 2t + 6 ) = 6t 2 + 18t 28w (2) 4w ( 3w - 7 ) = 12w 2 - (3) 5a ( 2a + 9 ) = 10a 2 + 45a (4) 2z ( 5z - 8 ) = 10z 2 - 16z

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**What Goes In The Box 2 ? (1) 3x ( 4x – 7 ) = – (2) 6w ( 8w + 3 ) = +**

(3) 2f ( 3f - 5 ) = 6f 2 – 10f (4) 8r ( 6r + 3 ) = 48r 2 + 24r (5) 3d ( 5d - 9 ) = 15d 2 – 27d (6) 8a ( 9a + 3 ) = 172a2 + 24a

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**More Than One Bracket. Consider the brackets below:**

Multiply out both brackets: 2( 3x + 6 ) + 2 ( 4x + 3 ) Gather like terms together. = 6x x + 6 = 6x + 8x Simplify by adding like terms. = 14x + 18 You have now multiplied out the brackets and simplified the expression.

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**Multiply out the brackets below and simplify :**

4 ( 3x – 5 ) + 2 ( 3x – 7 ) Solution. 4 ( 3x – 5 ) + 2 ( 3x – 7 ) = 12x – x – 14 = 12x + 6x – 20 – 14 = 18x – 34

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**Multiply out the brackets below and simplify :**

4 ( 2 b + 5 ) – 6 ( 3b – 4 ) Solution 4 ( 2 b + 5 ) – 6 ( 3b – 4 ) = 8b + 20 – 18b + 24 Remember that a negative times a negative makes a positive. = 8b – 18 b = – 10 b + 44

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**What Goes In The Box 3 ? Multiply out and simplify the brackets below:**

(1) 2 ( x + 4 ) + 3 ( x + 5) (5) 2 ( 3g – 4 ) + 2 ( 4g – 6 ) = 5x +23 = 14g -20 (2) 3 ( 2a + 5 ) + 4 ( 3a + 3 ) (6) 5 ( 3f – 6 ) – 4( 2 f – 6 ) = 7f – 6 = 18a + 27 (7) 3 ( 4t – 6 ) – 7 ( 6t – 8) ( 3) 4 ( 5b + 2 ) + 3 ( 2b + 7) = 26b + 29 = - 30t + 38

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