![Page 1: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/1.jpg)
Lesson 8-7
Multiplying Polynomials
![Page 2: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/2.jpg)
Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.
![Page 3: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/3.jpg)
![Page 4: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/4.jpg)
Objectives
• Multiply two binomials by using the FOIL method
• Multiply two polynomials by using the Distributive Property
![Page 5: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/5.jpg)
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.
![Page 6: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/6.jpg)
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
![Page 7: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/7.jpg)
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
F O I L
O I L
![Page 8: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/8.jpg)
Example 1Find (y + 8) (y – 4)
Method 1 Vertical
Multiply by y.
Add like terms.
Multiply by –4.
![Page 9: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/9.jpg)
Example 1 contFind
Method 2 Horizontal
Answer:
Distributive Property
Multiply.
Combine like terms.
Distributive Property
![Page 10: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/10.jpg)
Example 2aFind (z – 6)(z – 12)
Multiply.
Combine like terms.
Answer:
FF
O
O
I
I
L
L
![Page 11: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/11.jpg)
Example 2b
Find (5x – 4)(2x + 8)
Multiply.
Answer: Combine like terms.
F IO L
![Page 12: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/12.jpg)
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
![Page 13: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/13.jpg)
Example 3 cont
Original formula
Substitution
FOIL method
Multiply.
Combine like terms.
Distributive Property
Answer: The area of the triangle is square units.
![Page 14: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/14.jpg)
Example 4a
Find (3a + 4)(a2 – 12a + 1)
Distributive Property
Distributive Property
Answer: Combine like terms.
![Page 15: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/15.jpg)
Example 4b
Answer:Combine like terms.
Find (2b2 + 7b + 9)(b2 + 3b – 1)
Distributive Property
Distributive Property
![Page 16: Lesson 8-7 Multiplying Polynomials. Transparency 7 Click the mouse button or press the Space Bar to display the answers](https://reader035.vdocuments.net/reader035/viewer/2022070410/56649f1f5503460f94c3745e/html5/thumbnails/16.jpg)
Summary & Homework
• Summary:– 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