Multiplying Pairs of Brackets and Simplifying

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Multiplying Pairs of Brackets and Simplifying
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This means to multiply out a pair, or more, of
brackets. e.g. (ax b) (cx d).There are
3 ways of expanding brackets. They are

• The Box method
• The FOIL method
• The Separation method
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The Box Method
Multiply the individuals components together
(2a 3)(4a 2)
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The Box Method
(2a 3)(4a 2)
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We now have four separate values so (2a3)
(4a2) 8a2 12a 4a 6 This can be simplified
to give us our final answer (2a3) (4a2) 8a2
16a6
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Exercise

• (x 2)(x 1)
• (x 8)(x 2)
• (x 3)(x 3)
• (x 4)(x 5)
• (x 9)(x 2)
• (x 8)(x 3)
• (x 1)(x 6)
• (x 2)(x 8)
• (x 2)(5 x)
• (8 x)(1 x)

• x2 3x 2
• x2 10x 16
• x2 6x 9
• x2 x - 20
• x2 7x - 18
• x2 5x - 24
• x2 7x 6
• x2 6x 16
• -x2 3x 10
• x2 9x 8
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The FOIL method
FOIL stands for FIRST, OUTER, INNER, LAST And
refers to the order in which the values are
multiplied. For Example (x 3) (x -
5) FIRST, x x x x2 OUTER, x x -5
-5x INNER, 3 x x 3x LAST 3 x -5
-15 SIMPLIFY (x 3) (x - 5) x2 -2x -15
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Example 2 (2x - 3) (4x - 5) FIRST, 2x x 4x
8x2 OUTER, 2x x -5 -10x INNER, -3 x 4x
-12x LAST -3 x -5 15 SIMPLIFY (2x - 3)
(4x - 5) 8x2 -22x 15
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Exercise

• (x 5) (x 5)
• (2x 3) (5x 4)
• (x 3) (x 3)
• (3 x) (3 x)
• (2x 9) (2x 9)
• (x 9) (x 2)
• (5x 1) (6x 2)
• (3x 7) (2x 3)
• (2 x) (x 5)
• (8 2x) (1 x)

• x2 10x 25
• 10x2 7x 12
• x2 6x 9
• x2 6x 9
• 4x2 81
• x2 7x 18
• 30x2 4x 2
• 6x2 23x 21
• x2 3x 10
• 2x2 10x 8
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The Separation Method
Separating the brackets will often make life much
easier. For example (x 5) (2x 3) x(2x 3)
5(2x-3) Now we can multiply out the separate
brackets to obtain x(2x 3) 2x2 -3x and
5(2x-3) 10x -15 Adding these will give 2x2
-3x 10x -15 2x2 7x -15
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Example 2 (x2 2x - 5) (2x 3) x2(2x 3)
2x(2x-3) 5(2x-3) Now we can multiply out the
separate brackets to obtain x2(2x 3) 2x3 -
3x2 2x(2x 3) 4x2 6x and -5(2x-3) -10x
15 Adding these will give 2x3 -3x2 4x2 -6x -
10x 15 2x3 x2 - 16x 15
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Exercise

• (x 4) (x 4)
• (x 3) (5x 4)
• (x 3) (x 3)
• (3 x) (3 x)
• (2x 9) (2x 9)
• (2x 9) (4x 2)
• (6x 2) (x 1)
• (2x 7) (3x 3)
• (2 3x) (x2 4x)
• (8 x x2) (1 5x)

• x2 8x 16
• 5x2 11x 12
• x2 9
• 9 x2
• 4x2 36x 81
• 8x2 32x 18
• 6x2 4x 2
• 6x2 27x 21
• 3x3 10x2 8x
• 5x3 6x2 41x 8
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