 Mathematics
How would the expression x3 - 8 be rewritten using difference of cubes?

### Question Description

How would the expression x3 - 8 be rewritten using difference of cubes? Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

## Final Answer Thank you for the opportunity to help you with your question!

Use the formula of the differenceof cubes which is:   a^3 - b^3 = (a - b)(a^2 + ab + b^2).

So we compare the given expression x^3 - 8 to the left side of the formula: a^3 - b^3.

Here, we can see: a^3 = x^3  and  b^3 = 8. So we solve each equation by taking the cube root like this:

3th root(a^3) = 3th root(x^3) ---------> a = x

3th root(b^3) = 3th root(8) ------------> b = 2  (the cubic root of 8 is 2 since 2*2*2 = 8).

Then we enter x in place of a and 2 in place of b into the right side of the formula like this:

(a - b)(a^2 + ab + b^2) = (x - 2)(x^2 + 2x + 2^2)  = (x - 2)(x^2 + 2x + 4)   since 2^2 = 2*2 = 4.

So x^3 - 8 = (x - 2)(x^2 + 2x + 4).

Please let me know if you need any clarification. I'm always happy to answer your questions. DrMath (100)
Cornell University Anonymous
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