1. 1.3 – Day 1 Algebraic Expressions

2. 2 Objectives ► Adding and Subtracting Polynomials ► Multiplying Algebraic Expressions ► Special Product Formulas ► Factoring Common Factors ► Factoring Trinomials ► Special Factoring Formulas ► Factoring by Grouping Terms

3. 3 Algebraic Expressions Recall: polynomials Remember that the degree of a polynomial is the highest power of the variable that appears in the polynomial.

4. 4 Adding and Subtracting Polynomials

5. 5 We add and subtract polynomials using the properties of real numbers. The idea is to combine like terms (that is, terms with the same variables raised to the same powers) using the Distributive Property. For instance, 5x 7 + 3x 7 = (5 + 3)x 7 = 8x 7

6. 6 Example 1– Adding and Subtracting Polynomials (a)Find the sum (x 3 – 6x 2 + 2x + 4) + (x 3 + 5x 2 – 7x). (b) Find the difference (x 3 – 6x 2 + 2x + 4) – (x 3 + 5x 2 – 7x).

7. 7 Multiplying Algebraic Expressions

8. 8 To find the product of polynomials, we need to use the Distributive Property repeatedly, as well as the Laws of Exponents. (a + b)(c + d) = ac + ad + bc + bd

9. 9 Example 3 – Multiplying Polynomials Use the Distributive Property and the table method to find the product of: (2x + 3) (x 2 – 5x + 4) Method 1:

10. 10 Example 3 – Multiplying Polynomials Method 2: cont’d

11. 11 Special Product Formulas

12. 12 Example 4 – Using the Special Product Formulas Find the product of: (x 2 – 2) 3

13. 13 Factoring Common Factors (take out a GCF)

14. 14 Example 6 – Factor out a GCF Factor: (a) 8x 4 y 2 + 6x 3 y 3 – 2xy 4 (b) (2x + 4)(x – 3) – 5(x – 3)

15. 15 Practice: p. 32-33 #1, 7-21o, 27, 33, 37-43o, 51, 57-59o

16. 16 1.3 – Day 2 Algebraic Expressions

17. 17 Objectives ► Adding and Subtracting Polynomials ► Multiplying Algebraic Expressions ► Special Product Formulas ► Factoring Common Factors ► Factoring Trinomials ► Special Factoring Formulas ► Factoring by Grouping Terms

18. 18 Factoring Trinomials

19. 19 Example 9 – Factoring by Guess & Check Factor each expression. (a) x 2 – 2x – 3 (b) (5a + 1) 2 – 2(5a + 1) – 3 (c) 4x 2 – 4xy + y 2

20. 20 Special Factoring Formulas

21. 21 Special Factoring Formulas Some special algebraic expressions can be factored using the following formulas. The first three are simply Special Product Formulas written backward.

22. 22 Example 11 – Factoring Differences and Sums of Cubes Factor each polynomial. (a) 27x 3 – 1 (b) x 6 + 8

23. 23 Special Factoring Formulas When we factor an expression, the result can sometimes be factored further. In general, we first factor out common factors, then inspect the result to see whether it can be factored by any of the other methods of this section. We repeat this process until we have factored the expression completely.

24. 24 Example 13 – Factoring an Expression Completely Factor the expression completely: 2x 4 – 8x 2

25. 25 Factoring by Grouping Terms

26. 26 Example 15 – Factoring by Grouping Factor each polynomial. (a) x 3 + x 2 + 4x + 4 (b) x 3 – 2x 2 – 3x + 6

27. 27 Practice: p. 33 #61-81o, 85, 87, 91, 93, 107, 111, 117, 123-125