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Warm Up Simplify each expression. 1. 14 x + 15 y – 12 y + x 2. 9 xy + 2 xy – 8 xy

Warm Up Simplify each expression. 1. 14 x + 15 y – 12 y + x 2. 9 xy + 2 xy – 8 xy 3. –3( a + b ) +. 15 x + 3 y. 3 xy. –3 a – b + 10. Warm Up Continued Simplify. All variables represent nonnegative numbers. 4. 5. 6. Objective.

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Warm Up Simplify each expression. 1. 14 x + 15 y – 12 y + x 2. 9 xy + 2 xy – 8 xy

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  1. Warm Up Simplify each expression. 1. 14x + 15y – 12y + x 2. 9xy + 2xy – 8xy 3. –3(a + b) + 15x + 3y 3xy –3a – b + 10

  2. Warm Up Continued Simplify. All variables represent nonnegative numbers. 4. 5. 6.

  3. Objective Add and subtract radical expressions.

  4. Vocabulary like radicals

  5. Square-root expressions with the same radicand are examples of like radicals.

  6. Like radicals can be combined by adding or subtracting. You can use the Distributive Property to show how this is done: Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same.

  7. Helpful Hint Combining like radicals is similar to combining like terms.

  8. Directions: Add or subtract Remember: Look for “like” radicals

  9. A. Example 1 The terms are like radicals. B. The terms are unlike radicals. Do not combine.

  10. the terms are like radicals. Example 1 Continued… C. D. Identify like radicals. Combine like radicals.

  11. a. b. Example 2 The terms are like radicals. The terms are like radicals.

  12. The terms are like radicals. Example 2 Continued… c. The terms are like radicals. d. Combine like radicals.

  13. Sometimes radicals do not appear to be like until they are simplified, Simplify all radicals in an expression before trying to identify like radicals.

  14. Directions: Simplify, then add or subtract

  15. Example 3 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

  16. Example 4 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

  17. Remember! When you write a radicand as a product, make at least one factor a perfect square.

  18. Example 5 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

  19. Example 6 Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

  20. Lesson Summary Add or subtract. 1. 2. Simplify each expression. 3.

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