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Exercises Polynomials and factoring

Example 6.58 from Elementary Algebra, 6.4 Special Products

Special Products: example 6.58

Choose the appropriate pattern and use it to find the product:

ⓐ $(2 x - 3) (2 x + 3)$ ⓑ ${(8 x - 5)}^{2}$ ⓒ ${(6 m + 7)}^{2}$ ⓓ $(5 x - 6) (6 x + 5)$

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.

1
Solution
1. ⓐ $(2 x - 3) (2 x + 3)$ These are conjugates. They have the same first numbers, and the same last numbers, and one binomial is a sum and the other is a difference. It fits the Product of Conjugates pattern.
  
  This fits the pattern.
  
  Use the pattern.
  
  Simplify.
2. ⓑ ${(8 x - 5)}^{2}$ We are asked to square a binomial. It fits the binomial squares pattern.
  
  Use the pattern.
  
  Simplify.
3. ⓒ ${(6 m + 7)}^{2}$ Again, we will square a binomial so we use the binomial squares pattern.
  
  Use the pattern.
  
  Simplify.
4. ⓓ $(5 x - 6) (6 x + 5)$ This product does not fit the patterns, so we will use FOIL.
  
  $(5 x - 6) (6 x + 5)$
  
  Use FOIL. $30 x^{2} + 25 x - 36 x - 30$
  
  Simplify. $30 x^{2} - 11 x - 30$

Your turn

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

Choose the appropriate pattern and use it to find the product:

ⓐ $(9 b - 2) (2 b + 9)$ ⓑ ${(9 p - 4)}^{2}$ ⓒ ${(7 y + 1)}^{2}$ ⓓ $(4 r - 3) (4 r + 3)$

How did it go?

PreviousSpecial Products: example 6.57 Next Divide Monomials: example 6.59

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 6.4, 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.