(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.

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