7.8.-SPECIAL-PRODUCTS.ppt
- 1. Holt Algebra 1 7-8 Special Products of Binomials 7-8 Special Products of Binomials Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz
- 2. Holt Algebra 1 7-8 Special Products of Binomials Warm Up Simplify. 1. 42 3. (–2)2 4. (x)2 5. –(5y2) 16 49 4 x2 2. 72 6. (m2)2 m4 7. 2(6xy) 2(8x2) 8. 16x2 –25y2 12xy
- 3. Holt Algebra 1 7-8 Special Products of Binomials Find special products of binomials. Objective
- 4. Holt Algebra 1 7-8 Special Products of Binomials Vocabulary perfect-square trinomial difference of two squares
- 5. Holt Algebra 1 7-8 Special Products of Binomials Imagine a square with sides of length (a + b): The area of this square is (a + b)(a + b) or (a + b)2. The area of this square can also be found by adding the areas of the smaller squares and the rectangles inside. The sum of the areas inside is a2 + ab + ab + b2.
- 6. Holt Algebra 1 7-8 Special Products of Binomials This means that (a + b)2 = a2+ 2ab + b2. You can use the FOIL method to verify this: (a + b)2 = (a + b)(a + b) = a2 + ab + ab + b2 F L I O = a2 + 2ab + b2 A trinomial of the form a2 + 2ab + b2 is called a perfect-square trinomial. A perfect-square trinomial is a trinomial that is the result of squaring a binomial.
- 7. Holt Algebra 1 7-8 Special Products of Binomials Multiply. Example 1: Finding Products in the Form (a + b)2 A. (x +3)2 (a + b)2 = a2 + 2ab + b2 Use the rule for (a + b)2. (x + 3)2 = x2 + 2(x)(3) + 32 = x2 + 6x + 9 Identify a and b: a = x and b = 3. Simplify. B. (4s + 3t)2
- 8. Holt Algebra 1 7-8 Special Products of Binomials Multiply. Example 1C: Finding Products in the Form (a + b)2 C. (5 + m2)2
- 9. Holt Algebra 1 7-8 Special Products of Binomials Check It Out! Example 1 Multiply. A. (x + 6)2 B. (5a + b)2
- 10. Holt Algebra 1 7-8 Special Products of Binomials Check It Out! Example 1C Multiply. (1 + c3)2
- 11. Holt Algebra 1 7-8 Special Products of Binomials You can use the FOIL method to find products in the form of (a – b)2. (a – b)2 = (a – b)(a – b) = a2 – ab – ab + b2 F L I O = a2 – 2ab + b2 A trinomial of the form a2 – 2ab + b2 is also a perfect-square trinomial because it is the result of squaring the binomial (a – b).
- 12. Holt Algebra 1 7-8 Special Products of Binomials Multiply. Example 2: Finding Products in the Form (a – b)2 A. (x – 6)2 (a – b) = a2 – 2ab + b2 (x – 6) = x2 – 2x(6) + (6)2 = x – 12x + 36 Use the rule for (a – b)2. Identify a and b: a = x and b = 6. Simplify. B. (4m – 10)2
- 13. Holt Algebra 1 7-8 Special Products of Binomials Multiply. Example 2: Finding Products in the Form (a – b)2 C. (2x – 5y )2 D. (7 – r3)2
- 14. Holt Algebra 1 7-8 Special Products of Binomials Check It Out! Example 2 Multiply. a. (x – 7)2 b. (3b – 2c)2
- 15. Holt Algebra 1 7-8 Special Products of Binomials Check It Out! Example 2c Multiply. (a2 – 4)2
- 16. Holt Algebra 1 7-8 Special Products of Binomials (a + b)(a – b) = a2 – b2 A binomial of the form a2 – b2 is called a difference of two squares.
- 17. Holt Algebra 1 7-8 Special Products of Binomials Multiply. Example 3: Finding Products in the Form (a + b)(a – b) A. (x + 4)(x – 4) (a + b)(a – b) = a2 – b2 (x + 4)(x – 4) = x2 – 42 = x2 – 16 Use the rule for (a + b)(a – b). Identify a and b: a = x and b = 4. Simplify. B. (p2 + 8q)(p2 – 8q)
- 18. Holt Algebra 1 7-8 Special Products of Binomials Multiply. Example 3: Finding Products in the Form (a + b)(a – b) C. (10 + b)(10 – b)
- 19. Holt Algebra 1 7-8 Special Products of Binomials Check It Out! Example 3 Multiply. a. (x + 8)(x – 8) b. (3 + 2y2)(3 – 2y2)
- 20. Holt Algebra 1 7-8 Special Products of Binomials Check It Out! Example 3 Multiply. c. (9 + r)(9 – r)
- 21. Holt Algebra 1 7-8 Special Products of Binomials Write a polynomial that represents the area of the yard around the pool shown below. Example 4: Problem-Solving Application
- 22. Holt Algebra 1 7-8 Special Products of Binomials Check It Out! Example 4 Write an expression that represents the area of the swimming pool.
- 23. Holt Algebra 1 7-8 Special Products of Binomials