Sum of Two Cubes | MathHelp.com - By MathHelp.com
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In this example, weâre asked to factor x cubed â 8. Notice that x cubed is a perfect cube, and 8 is a perfect cube, because 8 is 2 times 2 times 2, or 2 cubed. So we have the difference of two cubes. To factor the difference of two cubes, we use the following formula: a cubed â b cubed can be factored as parentheses a â b times parentheses a squared + ab + b squared. And in this problem, since âaâ cubed is represented by x cubed, the value of a is x, and since b cubed is represented by 8, the value of b is 2. So, plugging x and 2 into the formula for a and b, we have parentheses x â 2 times parentheses x squared + x times 2 + 2 squared. And simplifying inside the second set of parentheses, we have parentheses x â 2 times parentheses x squared + 2x + 4, which is our final answer.
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