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**Multiplying Polynomials**

Lesson 8-7 Multiplying Polynomials

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

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**Objectives Multiply two binomials by using the FOIL method**

Multiply two polynomials by using the Distributive Property

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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.

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**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

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**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

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**Example 1 Find (y + 8) (y – 4) Method 1 Vertical Multiply by –4.**

Multiply by y. Add like terms.

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**Example 1 cont Find Method 2 Horizontal Distributive Property**

Multiply. Combine like terms. Answer:

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

Answer:

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

Combine like terms.

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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

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**Example 3 cont Original formula Substitution FOIL method Multiply.**

Combine like terms. Distributive Property Answer: The area of the triangle is square units.

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**Example 4a Find (3a + 4)(a2 – 12a + 1) Distributive Property**

Answer: Combine like terms.

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**Example 4b Find (2b2 + 7b + 9)(b2 + 3b – 1) Distributive Property**

Answer: Combine like terms.

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**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 even

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