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- 1. 6.10 Special Products<br />Objectives: <br /><ul><li>To square a binomial
- 2. To find products of the form (a + b)(a – b)</li></ul>Frameworks: 10.P.3<br />
- 3. How do we square a binomial?<br />(x + 3)2 = (x + 3)(x + 3)<br />FOIL: = x2 + 3x + 3x + 9<br /> = x2 + 6x + 9<br />Square of a sum: <br />(first term)2 + 2(first x last) + (last term)2<br />
- 4. Squaring a difference:<br />(3x - 5)2 = (3x - 5)(3x - 5)<br />FOIL: = 9x2 - 15x - 15x + 25<br /> = 9x2 - 30x + 25<br />Square of a difference: <br />(first term)2- 2(first x last) + (last term)2<br />
- 5. Notice<br />(x + 3)2 ≠ x2 + 9<br />(3x – 5)2≠ 9x2+ 25<br />When you square a binomial the product always contains three terms.<br />
- 6. Square of a Binomial<br />(a + b)2 = a2+ 2ab + b2<br />(a - b)2 = a2- 2ab + b2<br />
- 7. Try some:<br />(x – 8)(x - 8)<br />(2y + 1)2<br />(3x - 2)2<br />(5a + 1)2<br />
- 8. What about multiplying the sum and difference of the same 2 terms?<br /> (x + 6)(x - 6)<br />FOIL: = x2 - 6x + 6x - 36<br /> = x2 - 36<br />(first term)2 - (last term)2<br />Product of (a + b)(a – b): <br /> a2- b2<br />
- 9. Try some:<br />(c – 1)(c + 1)<br />(4x – 3)(4x + 3)<br />(3x + 2)(3x – 2)<br />
- 10. And now for something really fun:<br />(x – 5)2 = (x -8)(x + 8)<br /> x2– 10x + 25 = x2 – 64<br />- x2 = -x2<br />– 10x + 25 = – 64<br /> - 25 - 25<br /> - 10 x = - 89<br /> x = 8.9<br />
- 11. Try another fun one:<br />(x – 4)2 = (x -8)(x + 2)<br />
- 12. Turn to page 234<br />Do 1-4<br />

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