1. Subtraction of Polynomials Maths 8

2. Can you remove these tiles? Is this a positive or negative 1? Subtraction without the Zero principle Example : (3x -2) – (x - 1) 1. You represent the 1 st polynomial xxx -x Yes! 2x -1

3. Practice (5y + 3x) – (3y + 2x) (3x 2 - 2y - 6) – (2x 2 - y - 4) = 2y + x = x 2 - y - 2

4. Can you remove these tiles Can you remove a negative x and 3 positives? Using the Zero Principle Example : (3x -2) – (-x + 3) 1. You represent the 1 st polynomial xxx -x 1 1 1 NO! You need to use the zero principle.

5. Is there 1 negative and 3 positives to remove? Using the zero principle (3x -2) – (-x + 3) xxx -x 111 x 1 11 Yes! 4x -5

6. Practice (4x + 5) – (-2x – 3) (-2y – 3) – (4y + 1) (3x 2 – 2x + 4) – (-x 2 + x + 2) = 6x + 8 = - 6y - 4 = 4x 2 - 3x + 2

7. Can you remove these tiles? Is there a negative x and a negative 1 To Begin For example : (x + 1) – (- x - 1) 1. Represent the first polynomial x -x NO!

8. You have to remove these tiles. Is there a negative x and a negative 1? A method For example : (x + 1) – (- x - 1) x -x Use the zero principle. -x x Yes! I can now remove these tiles. 2x + 2

9. For example : (x + 1) – (- x - 1) x -x x 2x + 2

10. method For example: (x + 1) – (- x - 1) x -x x 2x + 2 In order to remove these tiles you can add the opposite, the opposite of –x -1 is x +1 Can you remove? -x

11. Add the Opposite Example : (x + 1) – (- x - 1) then….. ( x + 1 ) – ( - x – 1) = ( x + 1) + ( x + 1) = 2x + 2 Simplest form… Add the Opposite

12. Represent using “add the opposite” method (3x – 2) – (-x + 3) 1.Begin by representing the first term. 2.Then the second term 3.But, when subtracting, add the opposite if the second set of tiles. 4.Then add xxx x x (3x – 2) – (-x + 3) = (3x – 2) + (x - 3) = 4x - 5

13. Practice – Write the subtraction questions like addition questions (3x – 2) – (-2x + 3) = (2x + 3y + 5) – (3x – 2y – 1) = (-3x 2 – 2x + 4) – (-x 2 + 4x -3) = (3x – 2) + ( 2x – 3) (2x + 3y + 5) + (-3x + 2y + 1) (-3x 2 – 2x + 4) + (x 2 - 4x + 3)

14. Algetiles 1 x -x x x x2x2 -x 2 y-y y y y2y2 -y 2 x y xy -xy