Question

Factor the sum or difference of cubes. $$y^{3}+64$$

   Factor the sum or difference of cubes.
$$y^{3}+64$$

College Algebra

College Algebra

Ron Larson 9th Edition

Chapter 0, Problem 31

Instant Answer

Solved by Expert Teresa Fuston

10/13/2021

Step 1

In this case, we have $y^{3}+64$ which can be written as $y^{3}+4^{3}$. Show more…

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Factor the sum or difference of cubes. $$y^{3}+64$$

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Key Concepts

Algebraic Factorization

Algebraic factorization involves rewriting expressions as products of simpler factors. Utilizing formulas such as the sum or difference of cubes not only simplifies expressions but also aids in solving polynomial equations by breaking them down into their component factors.

Recognition of Perfect Cubes

Identifying when numbers or expressions are perfect cubes is a key step in applying the sum or difference of cubes formulas. Recognizing that 64 is a perfect cube, since 64 equals 4³, allows the expression y³ + 64 to be rewritten as y³ + 4³, which directly fits into the sum of cubes pattern.

Sum of Cubes Formula

The sum of cubes formula is an important algebraic identity used for factoring expressions of the form a³ + b³. It states that a³ + b³ can be factored as (a + b)(a² - ab + b²). This identity is a valuable tool in simplifying cubic expressions and solving related equations.

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