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Rewrite each expression without absolute value bars. ||-3|-|-7||
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 58
Factor using the formula for the sum or difference of two cubes.
Guida verificata passo dopo passo1
Recognize that the expression \(x^3 + 64\) is a sum of two cubes because \(64\) can be written as \$4^3$.
Recall the formula for the sum of two cubes: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$.
Identify \(a = x\) and \(b = 4\) in the expression \(x^3 + 4^3\).
Apply the sum of cubes formula: \((x + 4)(x^2 - 4x + 16)\).
Write the fully factored form as \((x + 4)(x^2 - 4x + 16)\).
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Sum of Cubes Formula
The sum of cubes formula is used to factor expressions of the form a^3 + b^3. It states that a^3 + b^3 = (a + b)(a^2 - ab + b^2). This formula helps break down cubic expressions into simpler polynomial factors.
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03:41
Special Products - Cube Formulas
Identifying Perfect Cubes
To apply the sum or difference of cubes formula, recognize each term as a perfect cube. For example, x^3 is the cube of x, and 64 is the cube of 4 since 4^3 = 64. Correct identification is essential for accurate factoring.
Video consigliato:
03:41Special Products - Cube Formulas
Factoring Polynomials
Factoring polynomials involves rewriting them as products of simpler polynomials. Using special formulas like the sum or difference of cubes simplifies complex expressions, making it easier to solve equations or analyze functions.
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07:30Introduction to Factoring Polynomials
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