# Multiplying Polynomials

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Multiplying Polynomials
Lesson 8-7 Multiplying Polynomials

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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

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

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

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