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Exercises Expressions, exponents and radicals

Example 7 from Algebra and Trigonometry, 1.5 Factoring Polynomials

Factoring a Difference of Cubes

Factor $8 x^{3} - 125.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Notice that $8 x^{3}$ and $125$ are cubes because $8 x^{3} = {(2 x)}^{3}$ and $125 = 5^{3} .$ Write the difference of cubes as $(2 x - 5) (4 x^{2} + 10 x + 25) .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor the difference of cubes: $1,000 x^{3} - 1.$

How did it go?

PreviousFactoring a Sum of Cubes Next Factoring an Expression with Fractional or Negative Exponents

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.