Question
Factor the difference of cubes. Select "Prime" if the polynomial cannot be factored.
Ask by Chan Coleman. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To factor the difference of cubes, use the formula \( a^3 - b^3 = (a - b)(a^2 + ab + b^2) \). Please provide the specific polynomial to factor or determine if it's prime.
Solution
To factor the difference of cubes, we use the formula:
\[
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
\]
Please provide the specific polynomial you would like to factor, and I will assist you in factoring it or determining if it is prime.
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Simplify this solution Mind Expander
The difference of cubes can be factored using the formula \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\). For example, if we have \(8 - 27\), we rewrite it as \(2^3 - 3^3\). Thus, we can factor it as \((2 - 3)(2^2 + 2 \cdot 3 + 3^2) = (-1)(4 + 6 + 9) = -1 \times 19\). In practical terms, recognizing perfect cubes can help you factor polynomials quickly. When faced with a cubic expression, always look for those cube roots first - it's like having an ace up your sleeve when playing a math game! And remember, if the expression isn’t a difference of cubes, take a step back because it might just be prime or need a different approach altogether.
