Question

Factor. $x^{3}-\frac{8}{27} y^{3}$

Name: Problem 130, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2022-02-10T01:43:47-08:00
Duration: 36 s
Channel: Erika Bustos
Description: Factor. x^3-(8)/(27) y^3

   Factor.
$x^{3}-\frac{8}{27} y^{3}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 130

Instant Answer

Solved by Expert Erika Bustos

02/10/2022

Step 1

The given expression can be written as $x^3 - \left(\frac{2}{3}y\right)^3$. Show more…

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Factor. $x^{3}-\frac{8}{27} y^{3}$

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Key Concepts

Difference of Cubes

This concept involves recognizing and factoring expressions of the form a³ - b³. The identity a³ - b³ = (a - b)(a² + ab + b²) is used to break down a cubic difference into simpler binomial and trinomial factors, making it easier to simplify or solve the expression.

Algebraic Factoring Techniques

Algebraic factoring techniques include identifying patterns in polynomial expressions, such as the difference of cubes, and applying corresponding formulas. Recognizing these patterns allows for the systematic reduction of complex expressions into products of simpler factors, which is essential for problem solving and equation analysis.

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