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\nFactor Using the Sum or Difference of Two Cubes Calculator
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How to Factor Using the Sum or Difference of Two Cubes
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The sum or difference of two cubes refers to algebraic expressions where two terms are perfect cubes and are added or subtracted. These expressions can be factored using specific formulas:
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Sum of Two Cubes
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The sum of two cubes formula is: $A^3 + B^3 = (A + B)(A^2 – AB + B^2)$
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Where:
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- $A$ is the cube root of the first term
- $B$ is the cube root of the second term
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Difference of Two Cubes
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The difference of two cubes formula is: $A^3 – B^3 = (A – B)(A^2 + AB + B^2)$
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Where:
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- $A$ is the cube root of the first term
- $B$ is the cube root of the second term
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Practical Examples
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Example 1: Sum of Cubes
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Factor $x^3 + 8$:
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- $A = x$
- $B = 2$
- $x^3 + 8 = (x + 2)(x^2 – 2x + 4)$
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Example 2: Difference of Cubes
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Factor $y^3 – 27$:
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- $A = y$
- $B = 3$
- $y^3 – 27 = (y – 3)(y^2 + 3y + 9)$
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