Page 99 - Math Course 2 (Book 1)

Multiplication by a Monomial

Mo. 3

Lesson 8 Simplify Expressions

Examples
KEY CONCEPTS:
1. Find the product of a monomial and a
polynomial. Simplify 3(2t – 4t – 15) + 6t(5t + 2).
2
2. Solve equations involving polynomials

2
3(2t – 4t – 15) + 6t(5t + 2).
MO. 3 - L8a
2
Product of a Monomial = 3(2t ) – 3(4t) – 3(15) + 6t(5t) + 6t(2)
Distributive Property
and a Polynomial

2
2
= 6t – 12t – 45 + 30t + 12t
Let’s Begin Product of Powers

2
2
= (6t + 30t ) + [(– 12t) + 12t] – 45
Multiply a Polynomial by a Commutative and Associative
Monomial 2
= 36t – 45
Answer Combine like terms.
Examples

2
Find 6y(4y – 9y – 7). Your Turn!
Method 1 Horizontal Multiply a Polynomial by a Monomial

2
2
6y(4y – 9y – 7) Find 3x(2x + 3x + 5).
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A. 6x + 9x + 15
2
2
3
= 6y(4y ) – 6y(9y) – 6y(7) Distributive Property. B. 6x + 9x + 15x
3
2
C. 5x + 6x + 8x
2
2
3
= 24y – 54y – 42y Multiply. D. 6x + 3x + 5
Answer
Method 2 Vertical
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Simplify 5(4y + 5y – 2) + 2y(4y +3).
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4y – 9y – 7
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A. 4y + 9y + 1
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B. 8y + 5y – 6
(x) 6y Distributive Property.
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C. 20y + 9y + 6
2
3
2
24y – 54y – 42y Multiply. D. 28y + 31y – 10
Answer
2
3
Answer 24y – 54y – 42y

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