1. Multiplying Polynomials; Special Products 5.5 1.Multiply a polynomial by a monomial. 2.Multiply binomials. 3. Multiply polynomials. 4.Determine the product when given special polynomial factors.

2. Objective 1 Multiply a polynomial by a monomial.

3. Multiply. 2p 6p 2 2p 2p –1 2p ∙ 6p 2 + 2p ∙ 2p+ 2p ∙ – 1

4. Multiplying a Polynomial by a Monomial Use the distributive property to multiply each term in the polynomial by the monomial.

5. When an equation in one variable is solved the answer is a point on a line. Multiply:

6. Objective 2 Multiply binomials.

7. Multiply. 7 x 7 3 x 3 x

8. Multiplying Polynomials 1. Multiply every term in the second polynomial by every term in the first polynomial. 2. Combine like terms.

9. Multiply. FOIL: First Outside Inside Last FirstOutsideInside Last 1 x Inside 1 (–5) Last 2x (–5) Outside 2x x First

10. When an equation in one variable is solved the answer is a point on a line. Multiply:

11. The product of two binomials can be shown in terms of geometry. 35 5x5x 7x7xx2x2 Length width = Sum of the areas of the four internal rectangles Combine like terms. 5 x x 7

12. Objective 3 Multiply polynomials.

13. Multiply. (–3) 2x 2 (–3) 3x (–3) 3 x 2x 2 x 3xx 3 Horizontal Multiplication

14. Multiply. Vertical Multiplication

15. When an equation in one variable is solved the answer is a point on a line. Multiply:

16. Objective 4 Determine the product when given special polynomial factors.

17. When an equation in one variable is solved the answer is a point on a line. Multiply:

18. Multiplying Conjugates If a and b are real numbers, variables, or expressions, then (a + b)(a – b) = a 2 – b 2. Conjugates: Binomials that differ only in the sign separating the terms. x + 9 and x – 9 2x + 3 and 2x – 3 –6x + 5 and –6x – 5

19. When an equation in one variable is solved the answer is a point on a line. Multiply: 2 ∙ 4a 2 ∙ – 5 n

20. Squaring a Binomial If a and b are real numbers, variables, or expressions, then (a + b) 2 = a 2 + 2ab + b 2 (a – b) 2 = a 2 – 2ab + b 2 or rewrite and foil !! Remember the shortcut

21. When an equation in one variable is solved the answer is a point on a line. Multiply:

22. Slide 5- 22 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5

23. Slide 5- 23 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5

24. Slide 5- 24 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5

25. Slide 5- 25 Copyright © 2011 Pearson Education, Inc. Multiply. a) b) c) d) 5.5