1. Multiplying polynomials In this PowerPoint presentation you will see two alternative approaches to polynomial multiplication. To see multiplication using a table click here. To see multiplication “in your head” click here.

2. Using a table x²x²3x3x-2 2x²2x² -x-x 4 Multiply x² + 3x 3x – 2 by 2x² – x + 4

3. Using a table x²x²3x3x-2 2x²2x² -x-x 4 Multiply x² by 2x²2x²

4. Using a table x²x²3x3x-2 2x²2x²2x42x4 -x-x 4 Multiply x² by 2x²

5. Using a table x²x²3x3x-2 2x²2x²2x42x4 -x-x 4 Multiply 3x 3x by 2x²2x²

6. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³ -x-x 4 Multiply 3x by 2x²

7. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³ -x-x 4 Fill in the rest of the table in the same way

8. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x 4 Fill in the rest of the table in the same way

9. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³ 4 Fill in the rest of the table in the same way

10. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x² 4 Fill in the rest of the table in the same way

11. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 4 Fill in the rest of the table in the same way

12. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x² Fill in the rest of the table in the same way

13. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x²12x Fill in the rest of the table in the same way

14. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x²12x-8 Fill in the rest of the table in the same way

15. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x²12x-8 Now add up all the terms in the table First the term in x4x4 (x² + 3x 3x – 2)(2x² - x + 4) = 2x42x4

16. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x²12x-8 Now add up all the terms in the table then the terms in x³x³ (x² + 3x – 2)(2x² - x + 4) = 2x 4 + 5x³5x³

17. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x²12x-8 Now add up all the terms in the table then the terms in x²x² (x² + 3x – 2)(2x² - x + 4) = 2x 4 + 5x³- 3x²

18. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x²12x-8 Now add up all the terms in the table (x² + 3x – 2)(2x² - x + 4) = 2x 4 then the terms in x + 5x³- 3x² + 14x

19. Using a table x²x²3x3x-2 2x²2x²2x42x4 6x³6x³-4x² -x-x-x³-x³-3x²2x2x 44x²4x²12x-8 Now add up all the terms in the table (x² + 3x – 2)(2x² - x + 4) = 2x 4 and finally the constant term + 5x³- 3x²+ 14x - 8

20. Multiplying polynomials To see this example of multiplication using a table again click here. To see multiplication “in your head” click here. To end this presentation click here.

21. Multiplying in your head Multiply x² + 3x 3x – 2 by 2x² – x + 4 (x² + 3x 3x – 2)(2x² – x + 4)4)

22. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Start by multiplying the first terms in each bracket to give a term in x4x4 = 2x42x4

23. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x³. There are two pairs. – x³x³ = 2x 4

24. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x³. There are two pairs. – x³– x³ + 6x³6x³ = 2x 4

25. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x². There are three pairs. – x³– x³+ 6x³ + 4x²4x² = 2x 4

26. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x². There are three pairs. – x³– x³+ 6x³+ 4x²= 2x 4 - 3x²3x²

27. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x². There are three pairs. – x³– x³+ 6x³+ 4x²- 3x² - 4x²4x² = 2x 4

28. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x. There are two pairs. = 2x 4 – x³– x³+ 6x³+ 4x²- 3x²- 4x² + 12x

29. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now look for pairs of terms which multiply together to give a term in x. There are two pairs. = 2x 4 – x³– x³+ 6x³+ 4x²- 3x²- 4x²+ 12x + 2x2x

30. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Finally multiply the last two terms in each bracket to give the constant term. = 2x 4 – x³– x³+ 6x³+ 4x²- 3x²- 4x²+ 12x+ 2x - 8

31. Multiplying in your head (x² + 3x – 2)(2x² – x + 4) Now simplify by collecting like terms. = 2x 4 – x³– x³+ 6x³+ 4x²- 3x²- 4x²+ 12x+ 2x- 8 = 2x4 2x4 + 5x³ - 3x² + 14x - 8

32. Multiplying polynomials To see multiplication using a table click here. To see this example of multiplication “in your head” again click here. To end this presentation click here.