1. 1 8-7 Multiplying Polynomials This presentation was created following the Fair Use Guidelines for Educational Multimedia. Certain materials are included under the Fair Use exemption of the U. S. Copyright Law. Further use of these materials and this presentation is restricted.

2. 2 Objectives  Students will multiply two binomials using the FOIL method.  Students will multiply two polynomials using the Distributive Property.

3. 3 Multiply Binomials  To multiply binomials, apply the Distributive Property twice.  FOIL: First Outside Inside Last

4. 4 Example 1 (y + 8)(y – 4) = yy + y-4 + 8y + 8 -4 First Outside Inside Last = y 2 – 4y + 8y – 32 = y 2 + 4y – 32

5. 5 Example 2 (z – 6)(z – 12) z 2 – 12z – 6z + 72 z 2 – 18z + 72

6. 6 Example 3 (5x – 4)(2x + 8) 10x 2 + 40x – 8x – 32 10x 2 + 32x – 32

7. 7 The Distributive Property  Multiply every term in the first set of parentheses by every term in the second set of parentheses. Example 4 (3a + 4)(a 2 – 12a + 1) = 3a a 2 + 3a -12a + 3a 1 + 4 a 2 + 4 -12a + 4 1 = 3a 3 – 36a 2 + 3a + 4a 2 – 48a + 4 = 3a 3 – 32a 2 – 45a + 4

8. 8 The Distributive Property  Example 5 (2x – 5)(3x 2 – 4x + 1) = 6x 3 – 8x 2 + 2x – 15x 2 + 20x – 5 = 6x 3 – 23x 2 + 22x – 5

9. 9 The Distributive Property  Example 6 (n 2 – 3n + 2)(n 2 + 5n – 4) = n 2 n 2 +n 2 5n + n 2 - 4 – 3nn 2 – 3n5n – 3n - 4 + 2n 2 + 25n + 2 - 4 = n 4 + 5n 3 – 4n 2 – 3n 3 – 15n 2 + 12n + 2n 2 + 10n – 8 = n 4 + 2n 3 – 17n 2 + 22n – 8