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Multiplying Out Brackets.

Explore how to multiply out double brackets step-by-step with illustrated examples and practice exercises. Learn the rules for dealing with negatives and positives to solve equations effectively.

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Multiplying Out Brackets.

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  1. Multiplying Out Brackets. Double Brackets.

  2. What Do Double Brackets Represent? A2 2x A1 Consider the area of this rectangle. A4 A3 3 A1 = 2x2 A2 = 12x x 6 A3 = 3x Total Area = 2x2 + 12x +3x +18 A4 = 18 Final Answer = 2x2 + 15x +18

  3. How To Multiply Out A Double Bracket. Consider: Golden Rule: Everything in the first bracket multiplies the second bracket. ( 2x + 3 ) ( x + 6) =2x (x + 6 ) +3 ( X + 6) = 2x2 + 12x + 3x + 18 = 2x2 + 15x + 18 The same as the area of the rectangle.

  4. What Goes In The Box? (4x + 3 ) ( 5x + 6) ( 5x + 6) + 3 ( 5x + 6) = 4x +24x +15x +18 =20x2 =20x2 +39x +18

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

  6. Brackets With Negatives & Positives. Using the rules you have just seen complete the following. ( 2x – 7 ) ( 5x – 4) ( 5x – 4) = 2x ( 5x – 4) -7 =10x2 - 8x - 35x + 28 - x + =10x2 43 28

  7. What Goes In The Box? ((3x – 4 ) ( 6x – 7) = 3x ( 6x – 7 ) - 4 ( 6x – 7 ) =18x2 +28 - 21x - 24x =18x2 -45x +28

  8. What Goes In The Box? ( 2x + 4 ) ( 3x – 8 ) ( 3x - 8 ) ( 3x - 8 ) = 2x + 4 -16x +12x = 6x2 -32 = 6x2 -4x -32

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