1. Multiplying Out Brackets. Double Brackets.

2. What Do Double Brackets Represent? Consider the area of this rectangle. x 6 2x 3 A1 A1 =2x 2 A2 A2 =12x A3 A3 =3x A4 A4 =18 Total Area = 2x 2 + 12x +3x +18 = 2x 2 + 15x +18 Final Answer

3. How To Multiply Out A Double Bracket. Consider: ( 2x + 3 ) ( x + 6) Golden Rule: Everything in the first bracket multiplies the second bracket. = 2x 2 The same as the area of the rectangle. =2x(x + 6 )+3( X + 6) + 12x+ 3x+ 18 + 15x+ 18

4. What Goes In The Box? (4x + 3 ) ( 5x + 6) ( 5x + 6) = 4x + 3 =20x 2 +24x+15x+18 =20x 2 +39x+18

5. Dealing With Negatives & Positives. You should know that : + x + =+ + x - =- - x + =- - x - =+ When you multiply. If the signs are the same you get a plus if they are different you get a negative. Now try these: (1) 4 x – 3 = (2) –2 x –5 = (3) - 7 x 2 = (4) 6 x 8 = (5) – 6 x – 9 = (6) 4 + – 3 = (7) 4 – – 3 = (8) – 5 – + 7 = (9) 6 + – 3 = (10) – 5 – – 4 = -12 10 -14 48 54 1 7 -12 3

6. Brackets With Negatives & Positives. Using the rules you have just seen complete the following. ( 2x – 7 ) ( 5x – 4) = 2x( 5x – 4)-7 ( 5x – 4) =10x 2 8x35x28 =10x 2 x 28 --+ - 43 +

7. What Goes In The Box? ((3x – 4 ) ( 6x – 7) = 3x( 6x – 7 )- 4( 6x – 7 ) =18x 2 - 21x- 24x +28 =18x 2 -45x+28

8. What Goes In The Box? ( 2x + 4 ) ( 3x – 8 ) = 2x ( 3x - 8 ) + 4 ( 3x - 8 ) = 6x 2 -16x+12x -32 = 6x 2 -4x -32