Textbook Question
Rewrite each expression using the distributive property and simplify, if possible. See Example 7. a + 7a
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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.2.91
Evaluate each expression. See Example 5. -4(9 - 8) + (-7) (2)³
Verified step by step guidance1
First, simplify the expression inside the parentheses. Calculate the value of \(9 - 8\).
Next, evaluate the exponentiation part of the expression. Calculate \$2^3$.
Multiply the results from the previous steps by their respective coefficients: multiply \(-4\) by the result of \(9 - 8\), and multiply \(-7\) by the result of \$2^3$.
After performing the multiplications, add the two products together to combine the terms.
Finally, simplify the sum to get the value of the entire expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Order of Operations
The order of operations dictates the sequence in which mathematical operations are performed: parentheses first, then exponents, followed by multiplication and division, and finally addition and subtraction. This ensures consistent and correct evaluation of expressions.
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Algebraic Operations on Vectors
Exponents
Exponents represent repeated multiplication of a base number. For example, 2³ means multiplying 2 by itself three times (2 × 2 × 2 = 8). Understanding exponents is essential for correctly simplifying expressions involving powers.
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4:28Introduction to Inverse Trig Functions
Multiplication of Negative Numbers
Multiplying negative numbers follows specific rules: a negative times a positive yields a negative, and a negative times a negative yields a positive. Recognizing these rules helps accurately simplify expressions with negative coefficients.
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5:02Multiplying Complex Numbers
Related Practice
Textbook Question
Find each product or quotient where possible. See Example 2. 2𝝅/( 2⁄3) (Leave 𝝅 in the answer.)
Textbook Question
Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 2 (x - 3y + 2z)
Textbook Question
Identify the property illustrated in each statement. Assume all variables represent real numbers. (7.5 - y) + 0 = 7.5 - y
Textbook Question
Identify the property illustrated in each statement. Assume all variables represent real numbers. (t - 6) • ( 1/(t-6)) = 1, if t - 6 ≠ 0
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Textbook Question
Simplify each expression. See Example 8. -2⁄3 (12w) (7z)