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tmlfan_179027
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How would you factor 8x^6+64? My text states that the answer is 8(x^2+2)(x^4-2x^2+4). How would you get to that?
Factoring a Sum of Cubes: How to Factor 8x^6+64?
- Context: High School
- Thread starter tmlfan_179027
- Start date
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SUMMARY
The expression 8x^6 + 64 can be factored as 8(x^2 + 2)(x^4 - 2x^2 + 4). The initial step involves factoring out the common coefficient of 8, simplifying the expression to a sum of cubes. Recognizing the sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), allows for the further factorization of the remaining polynomial.
PREREQUISITES- Understanding of polynomial factorization techniques
- Familiarity with the sum of cubes formula
- Basic algebraic manipulation skills
- Knowledge of factoring out common coefficients
- Study the sum of cubes formula in depth
- Practice factoring various polynomial expressions
- Explore advanced polynomial identities and their applications
- Learn about the differences between sum and difference of cubes
Students studying algebra, mathematics educators, and anyone interested in mastering polynomial factorization techniques.
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