Difference of Two Cubes | MathHelp.com

In this example, we’re asked to factor x cubed – 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 – b cubed can be factored as parentheses a – b times parentheses a squared + ab + b squared. And in this problem, since “a” 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 – 2 times parentheses x squared + x times 2 + 2 squared. And simplifying inside the second set of parentheses, we have parentheses x – 2 times parentheses x squared + 2x + 4, which is our final answer.

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How can you get the formula when you don't know it as (a-b)(a^2+ab+b^2)