2. To find products of the form (a + b)(a – b)Frameworks: 10.P.3

3. How do we square a binomial? (x + 3)2 = (x + 3)(x + 3) FOIL: = x2 + 3x + 3x + 9 = x2 + 6x + 9 Square of a sum: (first term)2 + 2(first x last) + (last term)2

4. Squaring a difference: (3x - 5)2 = (3x - 5)(3x - 5) FOIL: = 9x2 - 15x - 15x + 25 = 9x2 - 30x + 25 Square of a difference: (first term)2- 2(first x last) + (last term)2

5. Notice (x + 3)2 ≠ x2 + 9 (3x – 5)2≠ 9x2+ 25 When you square a binomial the product always contains three terms.

6. Square of a Binomial (a + b)2 = a2+ 2ab + b2 (a - b)2 = a2- 2ab + b2

7. Try some: (x – 8)(x - 8) (2y + 1)2 (3x - 2)2 (5a + 1)2

8. What about multiplying the sum and difference of the same 2 terms? (x + 6)(x - 6) FOIL: = x2 - 6x + 6x - 36 = x2 - 36 (first term)2 - (last term)2 Product of (a + b)(a – b): a2- b2

9. Try some: (c – 1)(c + 1) (4x – 3)(4x + 3) (3x + 2)(3x – 2)

10. And now for something really fun: (x – 5)2 = (x -8)(x + 8) x2– 10x + 25 = x2 – 64 - x2 = -x2 – 10x + 25 = – 64 - 25 - 25 - 10 x = - 89 x = 8.9

11. Try another fun one: (x – 4)2 = (x -8)(x + 2)

12. Turn to page 234 Do 1-4