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9.5 Factoring the Difference of Squares

9.5 Factoring the Difference of Squares. Difference of Two Squares. Must be in (a 2 - b 2 ) form a and b are any monomial (a 2 – b 2 ) = (a + b)(a – b). Example. 9a 2 – 16 (3a) 2 – (4) 2 (3a + 4)(3a – 4). Factor . Write in form. Factor the difference of squares. Answer: .

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9.5 Factoring the Difference of Squares

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  1. 9.5 Factoring the Difference of Squares

  2. Difference of Two Squares • Must be in (a2 - b2) form • a and b are any monomial (a2 – b2) = (a + b)(a – b)

  3. Example 9a2 – 16 (3a)2 – (4)2 (3a + 4)(3a – 4)

  4. Factor . Write in form Factor the difference of squares. Answer: Example 5-1a

  5. Factor . and Factor the difference of squares. Answer: Example 5-1a

  6. Factor each binomial. a. b. Answer: Answer: Example 5-1b

  7. Factor The GCF of and 27b is 3b. and Factor the difference of squares. Answer: Example 5-2a

  8. Factor Answer: Example 5-2b

  9. Factor The GCFofand 2500 is 4. and Factor the difference of squares. and Factor the difference of squares. Answer: Example 5-3a

  10. Factor Answer: Example 5-3b

  11. Factor Original Polynomial Factor out the GCF. Group terms with common factors. Factor each grouping. is the common factor. Factor the difference of squares,into . Answer: Example 5-4a

  12. Factor Answer: Example 5-4b

  13. Solve by factoring. Check your solutions. Original equation. and Factor the difference of squares. Zero Product Property or Solve each equation. Example 5-5a

  14. Answer: The solution set is Check each solution in the original equation. Example 5-5a

  15. Solve by factoring. Check your solutions. Original equation Subtract 3y from each side. The GCF of and 3y is 3y. and Example 5-5a

  16. Answer: The solution set is Check each solution in the original equation. or or Example 5-5a Applying the Zero Product Property, set each factor equal to zero and solve the resulting three equations.

  17. Solve each equation by factoring. Check your solutions. a. b. Answer: Answer: Example 5-5b

  18. a. Write an equation in terms of x that represents the area A of the figure after the corneris removed. b. What value of x will result in a figure that is the area of the original triangle? Show how you arrived at your answer. Example 5-6a Extended-Response Test ItemA square with side length x is cut from a right triangle shown below.

  19. a. The area of the triangle is or 64 square units and the area of the square is square units. Answer: b. Find x so that A is the area of the original triangle, Translate the verbal statement. Example 5-6a Read the Test Item A is the area of the triangle minus the area of the square that is to be removed. Solve the Test Item

  20. and Simplify. Subtract 48 from each side. Simplify. Factor the difference of squares. or Zero Product Property Solve each equation. Example 5-6a Answer: Since lengthcannot be negative, the only reasonable solution is 4.

  21. a. Write an equation in terms of x that represents the area A of the figure after thecorner is removed. b. What value of x will result in a figure that is of the area of the original square? Answer: Example 5-6b Extended-Response Test ItemA square with side length x is cut from the larger square shown below. Answer: 3

  22. Practice Problems Page 505 Problems 17-25, 34-41

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