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Examples and explanations on how to factor the sum and difference of cubes in algebra. It covers the process of finding the cubic roots and factoring out the greatest common factor (gcf). It also mentions the importance of factoring a difference of squares before a difference of cubes.
Typology: Summaries
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Sum or Difference of Cubes
A polynomial in the form a^3 + b^3 is called a sum of cubes. A polynomial in the form a^3 – b^3 is called a difference of cubes.
Both of these polynomials have similar factored patterns:
Example 1
Factor x^3 + 125. Find the cubic root of 125... √^3125 = 5; 5^3 = 125
Example 2
Factor 8 x^3 – 27. Find the cubic root of 8 and 27… √^3 8 = 2;^23 = 8, and √^3 27 = 3; 33 = 27
