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Exercises Polynomials and factoring

Example 7.58 from Elementary Algebra, 7.4 Factor Special Products

Factor Special Products: example 7.58

Factor: $5 m^{3} + 40 n^{3}$ .

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

Factor the common factor.

This binomial is a sum. The first and last terms are perfect cubes.

Write the terms as cubes.

Use the sum of cubes pattern.

Simplify.

Check. To check, you may find it easier to multiply the sum of cubes factors first, then multiply that product by 5. We’ll leave the multiplication for you.

$5 (\overset{}{m + 2 n}) (\overset{}{m^{2} - 2 m n + 4 n^{2}})$

Your turn

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

Factor: $500 p^{3} + 4 q^{3}$ .

How did it go?

PreviousFactor Special Products: example 7.57 Next General Strategy for Factoring Polynomials: example 7.59

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 7.4, 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.