step 1 So we're going to factor 27 x cubed minus 64 y cubed. So the cute root of 27 is 3. The cube root

Question

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

Name: Problem 375, Chapter 15: Algebra and Trigonometry
Uploaded: 2021-07-14T02:45:59-08:00
Duration: 1 min 12 s
Channel: Sherrie Fenner
Description: Factor 27 x^3-8 y^3

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

Algebra and Trigonometry

StemEZ 1st Edition

Chapter 15, Problem 375

Instant Answer

Solved by Expert Sherrie Fenner

07/14/2021

Step 1

We can rewrite the expression as $(3x)^3 - (2y)^3$. Show more…

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

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Key Concepts

Difference of Cubes

The difference of cubes is an algebraic identity that factors an expression of the form a³ - b³ into (a - b)(a² + ab + b²). This formula is fundamental in algebra, providing a systematic way to break down cubic expressions into simpler binomial and quadratic factors.

Rewriting Expressions as Perfect Cubes

A key step in applying the difference of cubes formula is rewriting each term as a perfect cube. This often involves expressing coefficients and variables in the form a³ and b³, which facilitates the direct application of the algebraic identity.

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