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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. R - Review of Basic Concepts문제 107
1장, 문제 107

Factor by any method. See Examples 1–7. 64+(3x+2)3

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1
Recognize that the expression is a sum of two terms: \(64\) and \((3x+2)^3\). Notice that \(64\) is a perfect cube since \(64 = 4^3\).
Rewrite the expression as a sum of cubes: \(4^3 + (3x+2)^3\).
Recall the sum of cubes factoring formula: \(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\).
Identify \(a = 4\) and \(b = (3x+2)\), then apply the formula: \((4 + (3x+2)) \left(4^2 - 4(3x+2) + (3x+2)^2\right)\).
Simplify the first factor and expand the terms inside the second factor to write the fully factored form.

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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 each perfect cubes added together. Recognizing the expression as a sum of cubes allows for straightforward factoring.
추천 영상:
03:41
Special Products - Cube Formulas

Identifying Perfect Cubes

To apply the sum of cubes formula, each term must be a perfect cube. For example, 64 is 4³, and (3x + 2)³ is already a cube. Recognizing these cubes is essential to rewrite the expression in a form suitable for factoring.
추천 영상:
03:41
Special Products - Cube Formulas

Polynomial Factoring Techniques

Factoring polynomials involves rewriting expressions as products of simpler polynomials. Techniques include factoring by grouping, special formulas like sum/difference of cubes, and recognizing patterns. Choosing the correct method simplifies solving or further manipulation.
추천 영상:
07:30
Introduction to Factoring Polynomials
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