1. 1 Multiplication of Brackets - FOIL Saturday, 05 March 2016 © RIVERMEAD Mathematics Department Aim of the lesson:Expand the product of two linear expressions. E.g. (x + 1)(x + 2) = x 2 + 3x + 2

2. 2 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) Remember the mnemonic F O I L = x² + 3x + 7x + 21 = x² + 10x + 21 First Outside InsideLast

3. 3 Multiply the brackets (x + 6)(x - 4) = x² - 4x + 6x - 24 = x² + 2x - 24 (x - 7)(x + 2) = x² + 2x - 7x - 14 = x² - 5x - 14 (x - 5)² = (x - 5)(x - 5) = x² - 5x + 25 = x² - 10x + 25 (1)(x + 3)(x + 6) (2) (x + 4)(x - 3) (3) (x – 3)(x + 5) (4) (x – 5)(x - 1) (5) (x + 2)² (6) (x – 4)² Left click to see answers x² + 9x + 18 x² + x + 12 x² + 2x – 15 x² – 6x + 5 x² + 4x + 4 x² - 8x + 16

4. 4 To see a dynamic display http://www.msubillings.edu/asc/algebra_helps.htm Then multiplying brackets - Foil

5. 5 Multiply the brackets (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 + 25 = 9x² - 30x + 25 (1)(4x + 3)(5x + 6) (2) (3x + 4)(2x - 3) (3) (5x – 3)(2x + 5) (4) (2x – 5)(2x - 1) (5) (5x + 2)² (6) (3x – 4)² Left click to see answers 20x² + 39x + 18 6x² - x - 12 10x² + 9x – 15 4x² – 12x + 5 25x² + 20x + 4 9x² - 24x + 16

6. 6 Multiply the brackets (5x + 4y)(3x – 4y) = 15x² - 20xy + 12xy - 16y² = 15x² - 8xy - 16y² (5x – 7y)(3x + y) = 15x² + 5xy - 21xy - 7y² = 15x² - 16xy - 7y² (4x – 5y)² = (4x – 5y)(4x – 5y) = 16x² - 20xy + 25y² = 16x² - 40xy + 25y² (1)(4x + y)(5x + 2y) (2) (3x + 2y)(3x – 2y) (3) (5x – 3y)(2x + 3y) (4) (2x – 5y)(3x - y) (5) (x + 2y)² (6) (3x – 7y)² Left click to see answers 20x² + 13xy + 2y² 9x² – 4y² 10x² + 9xy – 9y² 6x² – 17xy + 5y² x² + 4xy + 4y² 9x² - 42xy + 49y²

7. 7 Remember this topic as you will have one of these in your exam. Vocabulary:FOIL Product Expression