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Exercises Expressions, exponents and radicals

Example 5 from Algebra and Trigonometry, 1.5 Factoring Polynomials

Factoring a Difference of Squares

Factor $9 x^{2} - 25.$

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 $9 x^{2}$ and $25$ are perfect squares because $9 x^{2} = {(3 x)}^{2}$ and $25 = 5^{2} .$ The polynomial represents a difference of squares and can be rewritten as $(3 x + 5) (3 x - 5) .$

Your turn

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

Factor $81 y^{2} - 100.$

How did it go?

PreviousFactoring a Perfect Square Trinomial Next Factoring a Sum of Cubes

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.