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# 4 6multiplication formulas

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### 4 6multiplication formulas

1. 1. Multiplication Formulas
2. 2. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize.
3. 3. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other.
4. 4. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2),
5. 5. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c).
6. 6. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c). Note: The conjugate is different from the opposite. The opposite of (3x + 2) is (–3x – 2).
7. 7. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c). Note: The conjugate is different from the opposite. The opposite of (3x + 2) is (–3x – 2). I. Difference of Squares Formula
8. 8. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c). Note: The conjugate is different from the opposite. The opposite of (3x + 2) is (–3x – 2). I. Difference of Squares Formula (A + B)(A – B) Conjugate Product
9. 9. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c). Note: The conjugate is different from the opposite. The opposite of (3x + 2) is (–3x – 2). I. Difference of Squares Formula (A + B)(A – B) = A2 – B2 Conjugate Product Difference of Squares
10. 10. There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. I. Difference of Squares Formula (A + B)(A – B) = A2 – B2 Conjugate Product Difference of Squares To verify this : (A + B)(A – B) Multiplication Formulas For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c). Note: The conjugate is different from the opposite. The opposite of (3x + 2) is (–3x – 2).
11. 11. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c). Note: The conjugate is different from the opposite. The opposite of (3x + 2) is (–3x – 2). I. Difference of Squares Formula (A + B)(A – B) = A2 – B2 Conjugate Product Difference of Squares To verify this : (A + B)(A – B) = A2 – AB + AB – B2
12. 12. Multiplication Formulas There are some important patterns in multiplying expressions that it is worthwhile to memorize. The two binomials (A + B) and (A – B) are said to be the conjugate of each other. For example, the conjugate of (3x + 2) is (3x – 2), and the conjugate of (2ab – c) is (2ab + c). Note: The conjugate is different from the opposite. The opposite of (3x + 2) is (–3x – 2). I. Difference of Squares Formula (A + B)(A – B) = A2 – B2 Conjugate Product Difference of Squares To verify this : (A + B)(A – B) = A2 – AB + AB – B2 = A2 – B2
13. 13. Multiplication Formulas Here are some examples of squaring:
14. 14. Multiplication Formulas Here are some examples of squaring: (3x)2 =
15. 15. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2,
16. 16. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 =
17. 17. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2,
18. 18. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2
19. 19. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4.
20. 20. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2)
21. 21. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) (A + B)(A – B)
22. 22. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 (A + B)(A – B) = A2 – B2
23. 23. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2
24. 24. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2)
25. 25. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2
26. 26. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4
27. 27. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas
28. 28. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2
29. 29. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2 (A – B)2 = A2 – 2AB + B2
30. 30. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2 (A – B)2 = A2 – 2AB + B2 We may check this easily by multiplying,
31. 31. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2 (A – B)2 = A2 – 2AB + B2 We may check this easily by multiplying, (A + B)2 = (A + B)(A + B)
32. 32. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2 (A – B)2 = A2 – 2AB + B2 We may check this easily by multiplying, (A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2
33. 33. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2 (A – B)2 = A2 – 2AB + B2 We may check this easily by multiplying, (A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2
34. 34. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2 (A – B)2 = A2 – 2AB + B2 We may check this easily by multiplying, (A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2 We say that “(A + B)2 is A2, B2, plus twice A*B”,
35. 35. Multiplication Formulas Here are some examples of squaring: (3x)2 = 9x2, (2xy)2 = 4x2y2, and (5z2)2 = 25z4. Example A. Expand. a. (3x + 2)(3x – 2) = (3x)2 – (2)2 = 9x2 – 4 (A + B)(A – B) = A2 – B2 b. (2xy – 5z2)(2xy + 5z2) = (2xy)2 – (5z2)2 = 4x2y2 – 25z4 II. Square Formulas (A + B)2 = A2 + 2AB + B2 (A – B)2 = A2 – 2AB + B2 We may check this easily by multiplying, (A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2 = A2 + 2AB + B2 We say that “(A + B)2 is A2, B2, plus twice A*B”, and “(A – B)2 is A2, B2, minus twice A*B”.
36. 36. Example B. a. (3x + 4)2 Multiplication Formulas
37. 37. Example B. a. (3x + 4)2 (A + B)2 Multiplication Formulas
38. 38. Example B. a. (3x + 4)2 Multiplication Formulas (A + B)2 = A2 + 2AB + B2
39. 39. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 (A + B)2 = A2 + 2AB + B2
40. 40. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) (A + B)2 = A2 + 2AB + B2
41. 41. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 (A + B)2 = A2 + 2AB + B2
42. 42. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2
43. 43. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2
44. 44. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2
45. 45. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2
46. 46. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas
47. 47. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply.
48. 48. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49
49. 49. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1)
50. 50. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12
51. 51. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499
52. 52. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499 b. 52*48
53. 53. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499 b. 52*48 = (50 + 2)(50 – 2) = 502 – 22
54. 54. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499 b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496
55. 55. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499 b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496 c. 63*57 =
56. 56. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499 b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496 c. 63*57 = (60 + 3)(60 – 3) = 602 – 32
57. 57. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499 b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496 c. 63*57 = (60 + 3)(60 – 3) = 602 – 32 = 3,600 – 9 = 3,591
58. 58. Multiplication Formulas Example B. a. (3x + 4)2 = (3x)2 + 2(3x)(4) + 42 = 9x2 + 24x + 16 (A + B)2 = A2 + 2AB + B2 b. (3a – 5b)2 = (3a)2 – 2(3a)(5b) + (5b)2 = 9a2 – 30ab + 25b2 III. Some Applications of the Formulas We can use the above formulas to help us multiply. Example C. Calculate. Use the conjugate formula. a. 51*49 = (50 + 1)(50 – 1) = 502 – 12 = 2,500 – 1 = 2,499 b. 52*48 = (50 + 2)(50 – 2) = 502 – 22 = 2,500 – 4 = 2,496 c. 63*57 = (60 + 3)(60 – 3) = 602 – 32 = 3,600 – 9 = 3,591 The conjugate formula (A + B)(A – B) = A2 – B2 may be used to multiply two numbers of the forms (A + B) and (A – B) where A2 and B2 can be calculated easily.
59. 59. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”.
60. 60. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512
61. 61. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2
62. 62. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12
63. 63. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1)
64. 64. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100
65. 65. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601
66. 66. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492
67. 67. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2
68. 68. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12
69. 69. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1)
70. 70. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1) = 2,500 + 1 – 100
71. 71. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1) = 2,500 + 1 – 100 = 2,401
72. 72. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1) = 2,500 + 1 – 100 = 2,401 b. (50½) 2 = (50 + ½ )2
73. 73. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1) = 2,500 + 1 – 100 = 2,401 b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2
74. 74. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1) = 2,500 + 1 – 100 = 2,401 b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2 + 2 (½) (50)
75. 75. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1) = 2,500 + 1 – 100 = 2,401 b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2 + 2 (½) (50) = 2,500 + 1/4 + 50
76. 76. Multiplication Formulas The Squaring Formulas. “(A + B)2 is A2, B2, plus twice A*B”, “(A – B)2 is A2, B2, minus twice A*B”. Example D. Calculate. Use the squaring formulas. a. 512 = (50 + 1)2 = 502 + 12 + 2(50)(1) = 2,500 + 1 + 100 = 2,601 b. 492 = (50 – 1)2 = 502 + 12 – 2(50)(1) = 2,500 + 1 – 100 = 2,401 b. (50½) 2 = (50 + ½ )2 = 502 + ½ 2 + 2 (½) (50) = 2,500 + 1/4 + 50 = 2,550¼
77. 77. Multiplication Formulas Exercise. A. Calculate. Use the conjugate formula. 1. 21*19 2. 31*29 3. 41*39 4. 71*69 5. 22*18 6. 32*28 7. 52*48 8. 73*67 B. Calculate. Use the squaring formula. 9. 212 10. 312 11. 392 12. 692 13. 982 14. 30½2 15. 100½2 16. 49½2 C. Expand. 18. (x + 5)(x – 5) 19. (x – 7)(x + 7) 20. (2x + 3)(2x – 3) 21. (3x – 5)(3x + 5) 22. (7x + 2)(7x – 2) 23. (–7 + 3x )(–7 – 3x) 24. (–4x + 3)(–4x – 3) 25. (2x – 3y)(2x + 3y) 26. (4x – 5y)(5x + 5y) 27. (1 – 7y)(1 + 7y) 28. (5 – 3x)(5 + 3x) 29. (10 + 9x)(10 – 9x) 30. (x + 5)2 31. (x – 7)2 32. (2x + 3)2 33. (3x + 5y)2 34. (7x – 2y)2 35. (2x – h)2