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Multiplication of Brackets - FOIL
Thursday, 06 July 2017
© RIVERMEAD
Mathematics Department
Aim of the lesson:
Expand the product of two linear
expressions. E.g. (x + 1)(x + 2) = x2 + 3x + 2
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Reminder:
Multiply out the expression
3a(4a + 7)
3a(4a + 7) = 12a² + 21a
But what happens when there are 2 brackets
(x + 7)(x + 3) = x² + 3x + 7x + 21
= x² + 10x + 21
Remember the mnemonic
First
Outside
FOIL
Inside
Last
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(1) (x + 3)(x + 6)
Multiply the brackets
x² + 9x + 18
(x + 6)(x - 4)
= x² - 4x + 6x - 24
= x² + 2x - 24
(x - 7)(x + 2)
= x² + 2x - 7x - 14
= x²
(x - 5)²
- 5x - 14
= (x - 5)(x - 5)
= x² - 5x - 5x + 25
= x²
- 10x + 25
Left click to see answers
(2) (x + 4)(x - 3)
x² + x + 12
(3) (x – 3)(x + 5)
x² + 2x – 15
(4) (x – 5)(x - 1)
x² – 6x + 5
(5) (x + 2)²
x² + 4x + 4
(6) (x – 4)²
x² - 8x + 16
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To see a dynamic display
http://www.msubillings.edu/asc/algebra_helps.htm
Then multiplying brackets - Foil
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Multiply the brackets
(1) (4x + 3)(5x + 6)
20x² + 39x + 18
(2x + 6)(3x - 4) = 6x² - 8x + 18x - 24
= 6x² + 10x - 24
(4x - 7)(3x + 2) = 12x² + 8x - 21x - 14
= 12x² - 13x - 14
(3x - 5)²
= (3x - 5)(3x - 5)
= 9x² - 15x - 15x + 25
= 9x² - 30x + 25
(2) (3x + 4)(2x - 3)
6x² - x - 12
(3) (5x – 3)(2x + 5)
10x² + 9x – 15
(4) (2x – 5)(2x - 1)
4x² – 12x + 5
(5) (5x + 2)²
25x² + 20x + 4
Left click to see answers
(6) (3x – 4)²
9x² - 24x + 16
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Multiply the brackets
(1) (4x + y)(5x + 2y)
20x² + 13xy + 2y²
(5x + 4y)(3x – 4y) = 15x² - 20xy + 12xy - 16y²
= 15x² - 8xy - 16y²
(2) (3x + 2y)(3x – 2y)
9x² – 4y²
(5x – 7y)(3x + y) = 15x² + 5xy - 21xy - 7y² (3) (5x – 3y)(2x + 3y)
= 15x² - 16xy - 7y²
(4x – 5y)²
= (4x – 5y)(4x – 5y)
= 16x² - 20xy - 20xy + 25y²
= 16x² - 40xy + 25y²
10x² + 9xy – 9y²
(4) (2x – 5y)(3x - y)
6x² – 17xy + 5y²
(5) (x + 2y)²
x² + 4xy + 4y²
Left click to see answers
(6) (3x – 7y)²
9x² - 42xy + 49y²
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Remember this topic as you will
have one of these in your exam.
Vocabulary:
FOIL
Product
Expression
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