Question
Factor. \[ \begin{array}{l}r^{3}-8 \\ \text { SUBMIT ANSWER }\end{array} \]
Ask by Delgado Chadwick. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( r^3 - 8 = (r - 2)(r^2 + 2r + 4) \)
Solution
We recognize that \( r^3-8 \) is a difference of cubes since \( 8 = 2^3 \).
Using the difference of cubes factorization formula
\[
a^3 - b^3 = (a - b)(a^2 + ab + b^2),
\]
we set \( a = r \) and \( b = 2 \). Thus,
\[
r^3 - 8 = r^3 - 2^3 = (r-2)(r^2 + 2r + 4).
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To factor \( r^3 - 8 \), you can use the difference of cubes formula, which states that \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \). Here, \( a = r \) and \( b = 2 \), since \( 8 = 2^3 \). Applying the formula, we get: \[ r^3 - 8 = (r - 2)(r^2 + 2r + 4). \] Now the expression is fully factored! Remember, the quadratic part \( r^2 + 2r + 4 \) cannot be factored further using real numbers.
