(1) To square a binomial like (a + b)2, use the formula a2 + 2ab + b2. To square a difference like (a - b)2, use the formula a2 - 2ab + b2. (2) The product of two binomials of the form (a + b)(a - b) is a2 - b2. (3) Worked examples are provided to square binomials and multiply the sum and difference of the same two terms, along with practice problems for students to try.

1. 6.10 Special ProductsObjectives: To square a binomial

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 + 9Square 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 + 25Square of a difference: (first term)2- 2(first x last) + (last term)2

5. Notice(x + 3)2 ≠ x2 + 9(3x – 5)2≠ 9x2+ 25When 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)2Product 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 234Do 1-4