Textbook Question
Identify the property illustrated in each statement. Assume all variables represent real numbers. 6 • 12 + 6 • 15 = 6(12 + 15)
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.2.141
Simplify each expression. See Example 8. 10 - (4y + 8)
Verified step by step guidance1
Identify the expression to simplify: \(10 - (4y + 8)\).
Apply the distributive property to remove the parentheses by multiplying the minus sign with each term inside: \(10 - 4y - 8\).
Combine like terms (constants) by subtracting 8 from 10: \((10 - 8) - 4y\).
Simplify the constants to get \(2 - 4y\).
Write the final simplified expression as \(2 - 4y\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distributive Property
The distributive property allows you to multiply a single term across terms inside parentheses. For example, a(b + c) = ab + ac. In subtraction, it helps to remove parentheses by distributing the negative sign across the terms inside.
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Imaginary Roots with the Square Root Property
Combining Like Terms
Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies expressions by reducing the number of terms, making it easier to work with or solve.
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3:18Adding and Subtracting Complex Numbers
Simplifying Algebraic Expressions
Simplifying expressions means rewriting them in a simpler or more compact form without changing their value. This often involves applying properties like distribution and combining like terms to make the expression easier to understand or solve.
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6:36Simplifying Trig Expressions
Related Practice
Textbook Question
Simplify each expression. See Example 8. -12y + 4y + 3y + 2y
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
Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. -p² - 7q + r
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Textbook Question
Identify the property illustrated in each statement. Assume all variables represent real numbers. (5x) • (1/5x) = 5 ( x • 1/x )