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Exercises Polynomials and factoring

Example 7.44 from Elementary Algebra, 7.4 Factor Special Products

Factor Special Products: example 7.44

Factor: $36 x^{2} + 84 x y + 49 y^{2}$ .

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

Test each term to verify the pattern.

Factor.

Check by mulitplying.

${(6 x + 7 y)}^{2}$

${(6 x)}^{2} + 2 \cdot 6 x \cdot 7 y + {(7 y)}^{2}$

$36 x^{2} + 84 x y + 49 y^{2} ✓$

Your turn

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

Factor: $49 x^{2} + 84 x y + 36 y^{2}$ .

How did it go?

PreviousFactor Special Products: example 7.43 Next Factor Special Products: example 7.45

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.