Multiplying polynomials

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 Multiply x² + 3x – 2 by 2x² – x + 4

3. Using a table Multiply x² by 2x²

4. Using a table Multiply x² by 2x²

5. Using a table Multiply 3x by 2x²

6. Using a table Multiply 3x by 2x²

7. Using a table Fill in the rest of the table in the same way

8. Using a table Fill in the rest of the table in the same way

9. Using a table Fill in the rest of the table in the same way

10. Using a table Fill in the rest of the table in the same way

11. Using a table Fill in the rest of the table in the same way

12. Using a table Fill in the rest of the table in the same way

13. Using a table Fill in the rest of the table in the same way

14. Using a table Fill in the rest of the table in the same way

15. Using a table First the term in x4 Now add up all the terms in the table (x² + 3x – 2)(2x² - x + 4) = 2x4

16. Using a table Now add up all the terms in the table then the terms in x³ (x² + 3x – 2)(2x² - x + 4) = 2x4 + 5x³

17. Using a table Now add up all the terms in the table then the terms in x² (x² + 3x – 2)(2x² - x + 4) = 2x4 + 5x³ - 3x²

18. Using a table Now add up all the terms in the table then the terms in x (x² + 3x – 2)(2x² - x + 4) = 2x4 + 5x³ - 3x² + 14x

19. Using a table Now add up all the terms in the table and finally the constant term (x² + 3x – 2)(2x² - x + 4) = 2x4 + 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 – 2 by 2x² – x + 4 (x² + 3x – 2)(2x² – x + 4)

22. Multiplying in your head Start by multiplying the first terms in each bracket to give a term in x4 (x² + 3x – 2)(2x² – x + 4) = 2x4

23. Multiplying in your head Now look for pairs of terms which multiply together to give a term in x³. There are two pairs. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³

24. Multiplying in your head Now look for pairs of terms which multiply together to give a term in x³. There are two pairs. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³ + 6x³

25. Multiplying in your head Now look for pairs of terms which multiply together to give a term in x². There are three pairs. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³ + 6x³ + 4x²

26. Multiplying in your head Now look for pairs of terms which multiply together to give a term in x². There are three pairs. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³ + 6x³ + 4x² - 3x²

27. Multiplying in your head Now look for pairs of terms which multiply together to give a term in x². There are three pairs. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³ + 6x³ + 4x² - 3x² - 4x²

28. Multiplying in your head Now look for pairs of terms which multiply together to give a term in x. There are two pairs. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³ + 6x³ + 4x² - 3x² - 4x² + 12x

29. Multiplying in your head Now look for pairs of terms which multiply together to give a term in x. There are two pairs. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³ + 6x³ + 4x² - 3x² - 4x² + 12x + 2x

30. Multiplying in your head Finally multiply the last two terms in each bracket to give the constant term. (x² + 3x – 2)(2x² – x + 4) = 2x4 –x³ + 6x³ + 4x² - 3x² - 4x² + 12x + 2x - 8

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

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