Textbook Question
CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. 8x³ - 27 A. (3 - 2x) (9 + 6x + 4x²) b. 8x³ + 27 B. (2x - 3) (4x² + 6x + 9) c. 27 - 8x³ C. (2x + 3) (4x² - 6x + 9)
Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem R.2.143
Simplify each expression. See Example 8. 10x (3)(y)
Verified step by step guidance1
Identify the expression given: \$10x (3)(y)$. This involves multiplication of constants and variables.
Rewrite the expression by grouping the constants and variables separately: \((10 \times 3) \times (x \times y)\).
Multiply the constants together: \(10 \times 3 = 30\).
Combine the variables by multiplication: \(x \times y = xy\).
Write the simplified expression by combining the results: \$30xy$.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Algebraic Simplification
Algebraic simplification involves combining like terms and applying arithmetic operations to rewrite expressions in a simpler form. In this context, it means multiplying constants and variables correctly to reduce the expression to its simplest equivalent.
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Algebraic Operations on Vectors
Multiplication of Variables and Constants
When multiplying variables and constants, multiply the numerical coefficients and then write the variables together. For example, multiplying 10x by 3y involves multiplying 10 and 3 to get 30, and then combining the variables x and y as xy.
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5:28Equations with Two Variables
Understanding Notation and Expression Structure
Recognizing how expressions are written, such as 10x(3)(y), helps in correctly applying operations. Parentheses indicate multiplication, so the expression means 10 times x times 3 times y, which guides the order and method of simplification.
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06:01i & j Notation
Related Practice
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The opposite, or negative, of a number is its _______.
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Textbook Question
Rewrite each expression using the distributive property and simplify, if possible. See Example 7. x + x
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Textbook Question
Rewrite each expression using the distributive property and simplify, if possible. See Example 7. -(2d - f)
Textbook Question
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = (x + 4)² is obtained by shifting the graph of y = x² to the ___ 4 units.
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Textbook Question
Find the given distances between points P, Q, R, and S on a number line, with coordinates -4, -1, 8, and 12, respectively. See Example 3. d (Q, R)
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