Page 103 - Math Course 2 (Book 1)

Polynomials: Multiplication

Mo. 3

Lesson 9

KEY CONCEPTS:
1. Multiply two polynomials by using the Let’s Begin
Distributive Property.
2. Multiply two binomials by using the FOIL
method. The Distributive Property

Examples
MO. 3 - L9a

Multiplying Polynomials: Find (y + 8)(y – 4).

The Distributive Property Method 1 Vertical

Key Concept Multiply by –4.
Multiply by y.
Combine like terms.

FOIL Method y + 8
(×) y – 4
–4y – 32 –4(y + 8) = –4y – 32
Words To multiply two binomials, f nd the sum y² + 8y y(y + 8) = y2 + 8y
of the products of
y² + 4y – 32
F the First terms,
O the Outer terms, Method 2 Horizontal
I the Inner terms, and
L the Last terms.
(y + 8)(y – 4) = y(y – 4) + 8(y –4) Distributive
Property.

Example Product of Product of Product of Product of = y(y) – y(4) + 8(y) – 8(4)
First Outer Inner Last Distributive
Terms Terms Terms Terms Property.
F L ? ? ? ?
2
= y – 4y + 8y – 32 Multiply.
(x + 3) (x – 2) = (x) (x) + (–2)(x) + (3)(x) + (3) (–2)
2
I = x – 2x + 3x – 6 = y + 4y – 32 Combine like
2
0 terms.
2
= x + x – 6
2
Answer y + 4y – 32

2
Find (3a + 4)(a – 12a + 1).
2
(3a + 4)(a – 12a + 1)
2
2
= 3a(a – 12a + 1) + 4(a – 12a + 1) Distributive Property.
3
2
2
= 3a – 36a + 3a + 4a – 48a + 4 Distributive Property.
3
= 3a – 32a² – 45a + 4 Combine like terms.
3
Answer 3a – 32a² – 45a + 4

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