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Evaluate each expression. See Example 5. -|-2|
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 61
Find each product. See Example 5. (2x + 5)³
Guida verificata passo dopo passo1
Recognize that the expression \((2x + 5)^3\) is a binomial raised to the third power, which means you need to expand it using the binomial cube formula.
Recall the binomial cube formula: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). Here, identify \(a = 2x\) and \(b = 5\).
Calculate each term separately: \(a^3 = (2x)^3\), \(3a^2b = 3 \times (2x)^2 \times 5\), \(3ab^2 = 3 \times (2x) \times 5^2\), and \(b^3 = 5^3\).
Write the expanded form by summing all the terms: \((2x)^3 + 3(2x)^2(5) + 3(2x)(5)^2 + 5^3\).
Simplify each term by performing the powers and multiplications, then combine all terms to get the final expanded polynomial.
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Binomial Expansion
Binomial expansion is the process of expanding expressions raised to a power, such as (a + b)³. It involves applying the binomial theorem or using formulas to express the power as a sum of terms involving powers of each component.
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Rationalizing Denominators Using Conjugates
Binomial Theorem
The binomial theorem provides a formula to expand expressions of the form (a + b)^n. It uses binomial coefficients, often represented by combinations, to determine the coefficients of each term in the expanded form.
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5:19Solving Right Triangles with the Pythagorean Theorem
Algebraic Multiplication of Polynomials
Multiplying polynomials involves distributing each term in one polynomial to every term in the other. For powers like cubes, this means repeated multiplication and combining like terms to simplify the expression.
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04:12Algebraic Operations on Vectors
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