교과서 질문
Add or subtract, as indicated. See Example 6. √6 + √6
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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
1장, 문제 89
Factor each polynomial completely. See Example 6. 8t³ + 125
검증된 단계별 안내1
Recognize that the polynomial \(8t^{3} + 125\) is a sum of cubes because \(8t^{3} = (2t)^{3}\) and \(125 = 5^{3}\).
Recall the sum of cubes factoring formula: \(a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})\).
Identify \(a = 2t\) and \(b = 5\) in the expression \(8t^{3} + 125\).
Apply the formula: write the factorization as \((2t + 5)((2t)^{2} - (2t)(5) + 5^{2})\).
Simplify the terms inside the second parenthesis to get \((2t + 5)(4t^{2} - 10t + 25)\).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Sum of Cubes Formula
The sum of cubes formula states that a³ + b³ = (a + b)(a² - ab + b²). It is used to factor expressions where two terms are both perfect cubes added together. Recognizing 8t³ and 125 as cubes (2t)³ and 5³ allows applying this formula to factor the polynomial.
추천 영상:
2:25
Verifying Identities with Sum and Difference Formulas
Identifying Perfect Cubes
A perfect cube is a number or expression raised to the third power, such as 8 = 2³ or t³. Identifying each term as a perfect cube is essential before applying the sum or difference of cubes formulas. This step ensures the correct factorization method is used.
추천 영상:
6:50Convert Equations from Polar to Rectangular
Polynomial Factoring Techniques
Factoring polynomials involves rewriting them as products of simpler polynomials. Techniques include factoring out common factors, grouping, and special formulas like sum/difference of cubes. Understanding these methods helps break down complex expressions into factors.
추천 영상:
6:08Factoring
관련 실천
교과서 질문
Simplify each complex fraction. See Examples 5 and 6. [(y + 3)/y − 4/(y − 1)] / [(y/y + 1/y) / (y − 1) + 1/y]
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교과서 질문
(Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula.
Distance = (7 − x) / (0.639x + 1.75)
For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), and the distance from the origin is
Distance ≈ (7 − 0.6) / (0.639 × 0.6 + 1.75) ≈ 3, which represents 3000 mi. (Data from The World Almanac and Book of Facts.) What is the distance from the origin of the Nile when the river has an altitude of 7000 ft?
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교과서 질문
Add or subtract, as indicated. See Example 6. √6 + √7
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교과서 질문
Simplify each inequality if needed. Then determine whether the statement is true or false. 7 ≤ 7
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교과서 질문
Simplify each inequality if needed. Then determine whether the statement is true or false. 0 ≤ -5
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