Multiplying Polynomials

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Presentation transcript:

Multiplying Polynomials Lesson 8-7 Multiplying Polynomials

Click the mouse button or press the Space Bar to display the answers. Transparency 7

Transparency 7a

Objectives Multiply two binomials by using the FOIL method Multiply two polynomials by using the Distributive Property

Vocabulary FOIL method – to multiply two binomials, find the sum of the products of the First terms, the Outer terms, the Inner terms, and the Last terms.

Multiplying Polynomials Use the Distributive Property of Equality Simplify by combining like terms Example: (2x – 1)(3x + 4) = 2x(3x) – 1(3x) + 2x(4) – 1(4) = 6x2 – 3x + 8x – 4 = 6x2 + 5x – 4

FOIL Method First terms, Outside terms, Inside terms, Last Terms Example: (2x – 1)(3x + 4) = 2x(3x) + 2x(4) – 1(3x) – 1(4) = 6x2 + 8x – 3x + 4 = 6x2 + 5x – 4 F O I L F O I L

Example 1 Find (y + 8) (y – 4) Method 1 Vertical Multiply by –4. Multiply by y. Add like terms.

Example 1 cont Find Method 2 Horizontal Distributive Property Multiply. Combine like terms. Answer:

Example 2a Find (z – 6)(z – 12) F L I O Multiply. Combine like terms. Answer:

Example 2b Find (5x – 4)(2x + 8) F I O L Multiply. Answer: Combine like terms.

Example 3 Geometry The area A of a triangle is one-half the height h times the base b. Write an expression for the area of the triangle. Identify the height and the base. Now write and apply the formula. Area equals one-half height times base. A h b

Example 3 cont Original formula Substitution FOIL method Multiply. Combine like terms. Distributive Property Answer: The area of the triangle is square units.

Example 4a Find (3a + 4)(a2 – 12a + 1) Distributive Property Answer: Combine like terms.

Example 4b Find (2b2 + 7b + 9)(b2 + 3b – 1) Distributive Property Answer: Combine like terms.

Summary & Homework Summary: Homework: The FOIL method is the sum of the products of the first terms F, the outer terms O, the inner term I, and the last terms L The Distributive Property can be used to multiply any two polynomials Homework: Pg. 455 20-38 even