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Algebra 2. Do this First! For Review Algebra 2.

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Presentation on theme: "Algebra 2. Do this First! For Review Algebra 2."— Presentation transcript:

1 Algebra 2

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4 Do this First! For Review

5 Algebra 2

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10 Binomial Radical Expressions Section 7-3 Binomial Radical Expressions Lesson 7-3

11 Algebra 2 Objectives To add and subtract radical expressions Binomial Radical Expressions Lesson 7-3

12 Algebra 2 Adding or Subtracting Radical Expressions Binomial Radical Expressions Lesson 7-3

13 Algebra 2 Binomial Radical Expressions Lesson 7-3

14 Algebra 2 Binomial Radical Expressions Lesson 7-3

15 Algebra 2 Adding or Subtracting Radical Expressions Binomial Radical Expressions Lesson 7-3

16 Algebra 2 Binomial Radical Expressions Lesson 7-3

17 Algebra 2 Binomial Radical Expressions Lesson 7-3

18 Algebra 2 Binomial Radical Expressions Lesson 7-3 Add or subtract if possible. a. 7 xy + 3 xy Distributive Property 7 xy + 3 xy = (7 + 3) xy = 10 xy Subtract. 33 b. 2 x – 2 5 The radicals are not like radicals. They cannot be combined. Additional Examples

19 Algebra 2 Binomial Radical Expressions Lesson 7-3 The rectangular window shown below is made up of three equilateral triangles and two right triangles. The equilateral triangles have sides of length 4 feet. What is the perimeter of the window? So the window’s height is 2 3 ft. The length of the window is 8 ft. The perimeter is 2(2 3 + 8) ft or 16 + 4 3 ft. The height of an equilateral triangle with side length 4 ft is 2 3 ft. Additional Examples

20 Algebra 2 Simplify 3 20 – 45 + 4 80. Binomial Radical Expressions Lesson 7-3 3 20 – 45 + 4 80 = 3 2 2 5 – 3 2 5 + 4 4 2 5Factor each radicand. Simplify each radical.= 3 2 5 – 3 5 + 4 4 5 Multiply.= 6 5 – 3 5 + 16 5 Use the Distributive Property.= (6 – 3 + 16) 5 = 19 5 Additional Examples

21 Algebra 2 Review FOIL Method Binomial Radical Expressions Lesson 7-3

22 Algebra 2 Review FOIL Method Binomial Radical Expressions Lesson 7-3

23 Algebra 2 Binomial Radical Expressions Lesson 7-3 Multiply (2 + 4 3)(1 – 5 3). Use FOIL. (2 + 4 3)(1 – 5 3) = 2 1 – 2 5 3 + 4 3 1 – 4 3 5 3 = 2 + (4 – 10) 3 – 60Distributive Property = –58 – 6 3 Additional Examples

24 Algebra 2 Multiply Binomial Radical Expressions Lesson 7-3

25 Algebra 2 Binomial Radical Expressions Lesson 7-3

26 Algebra 2 Multiply Binomial Radical Expressions Lesson 7-3

27 Algebra 2 Binomial Radical Expressions Lesson 7-3 Multiply (3 + 7)(3 – 7). = 9 – 7 = 2 (a + b)(a – b) = a 2 – b 2 (3 + 7)(3 – 7) = 3 2 – ( 7) 2 Additional Examples

28 Algebra 2 Multiply Binomial Radical Expressions Lesson 7-3

29 Algebra 2 Conjugates Binomial Radical Expressions Lesson 7-3

30 Algebra 2 Rationalizing the Denominator When the denominator to be rationalized has two terms, we chose a symbol for 1 that are conjugates of each other. Binomial Radical Expressions Lesson 7-3

31 Algebra 2 Rationalizing the Denominator Binomial Radical Expressions Lesson 7-3

32 Algebra 2 Rationalizing the Denominator Binomial Radical Expressions Lesson 7-3

33 Algebra 2 Binomial Radical Expressions Lesson 7-3 Rationalize the denominator of 2 – 3 4 + 3 2 – 3 4 + 3 = 2 – 3 4 + 3 4 – 3 4 – 3 is the conjugate of 4 + 3.= 2 – 3 4 + 3 4 – 3 Multiply. 4 2 – ( 3) 2 8 – 2 3 – 4 3 + ( 3) 2 = Simplify. 11 – 6 3 13 = Additional Examples

34 Algebra 2 Now you can: Add and Subtract Radical Expressions FOIL/Distribute Radical Expressions Rationalize Binomial Radical Expressions Binomial Radical Expressions Lesson 7-3

35 Algebra 2 xx2x2 x3x3 x4x4 x5x5 2481632 392781243 416642561024 525125625 636216 749343 864512

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