1. Multiplying Polynomials MATH 017 Intermediate Algebra S. Rook

2. 2 Overview Section 5.4 in the textbook –Multiply by monomials –Multiply binomials –Square binomials –Multiply (a + b)(a – b) –Multiply more than two polynomials

3. Multiplying by a Monomial

4. 4 Use the distributive property Simplify using exponent rules

5. 5 Multiplying by a Monomial (Example) Ex 1: Multiply:

6. 6 Multiplying by a Monomial (Example) Ex 2: Multiply:

7. Multiply Binomials

8. 8 Multiplying Polynomials in General To multiply (4x + 3)(2x 2 – 3x + 7), we use the distributive property = 4x(2x 2 – 3x + 7) + 3(2x 2 – 3x + 7) Simplify and combine any like terms

9. 9 Multiplying Polynomials in General (Example) Ex 3: Multiply (3x 2 + 4x – 5)(3x + 2)

10. 10 Multiplying Binomials Recall that a binomial is a polynomial with 2 terms Can also use the distributive property A helpful pneumonic is FOIL (essentially the distributive property) F irst O uter I nner L ast

11. 11 Multiplying Binomials (Example) Ex 4: Multiply: (4x + 5)(3x - 2)

12. 12 Multiplying Binomials (Example) Ex 5: Multiply: (2x - 7)(x - 8)

13. Square Binomials

14. 14 Square Binomials First expand: (a + b) 2 = (a + b)(a + b) Finally use FOIL Do NOT just square each of the individual terms! (a + b) 2 ≠ a 2 + b 2

15. 15 Square Binomials (Example) Ex 6: Multiply: (3x + 2y) 2

16. 16 Square Binomials (Example) Ex 7: Multiply: (4x – 5) 2

17. Multiply (a + b)(a – b)

18. 18 Multiply (a + b)(a – b) A special product Use FOIL to simplify The O and the I terms cancel

19. 19 Multiply (a + b)(a – b) (Example) Ex 8: Multiply (m – 3n)(m + 3n)

20. 20 Multiply (a + b)(a – b) (Example) Ex 9: Multiply (2r 4 + 5s 2 )(2r 4 – 5s 2 )

21. Multiply More than Two Polynomials

22. 22 Multiply More than Two Polynomials Multiply the first two polynomials using the techniques discussed thus far Use the distributive property to multiply the result by the last polynomial Simplify

23. 23 Multiply More than Two Polynomials (Example) Ex 10: Multiply (x + 2)(x – 7)(x + 1)

24. 24 Multiply More than Two Polynomials (Example) Ex 11: Multiply (x + 4) 2 (7x – 2)

25. 25 Summary After studying these slides, you should know how to do the following: –Multiply by monomials –Multiply binomials –Square binomials –Multiply (a + b)(a – b) –Multiply more than two polynomials