How to Factor the Sum or Difference of Cubes
To successfully factor a binomial that is a sum or difference of cubes, follow this five-step procedure:
- Check the pattern: Determine if the binomial is a sum or a difference, and verify that both the first and last terms are perfect cubes.
- Rewrite as cubes: Express both terms explicitly as perfect cubes, in the form and , to clearly identify the values of the bases and .
- Apply the formula: Substitute the bases into the sum of cubes pattern or the difference of cubes pattern .
- Simplify: Calculate the squares and products inside the parentheses to simplify the resulting trinomial factor.
- Verify: Check your work by multiplying the binomial and trinomial factors to ensure their expanded product equals the original binomial expression.
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A logistics coordinator is calculating the volume difference between two cubic storage containers, represented by the expression a^3 - b^3. To simplify the inventory records, the coordinator needs to identify the correct factored form of this expression. Which of the following formulas represents the Difference of Cubes Pattern?
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How to Factor the Sum or Difference of Cubes
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A construction supervisor is calculating the volume of soil removed for two cubic pits. The total volume is represented by the expression v^3 + 8. Arrange the following steps in the correct order to factor this sum of cubes.
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