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乘法公式

乘法公式. 國中數學 第 3 冊. （ a + b ）（ c + d ） ＝ ac + bc + ad + bd. a ＋ b. a. b. ac. ( a + b ) × c. bc. c. c ＋ d. ad. bd. ( a + b ) × d. d. （ a + b ） × （ c + d ）. = （ a + b ） × c + （ a + b ） × d. = ac + bc + ad + bd. 4 1 × 5 3. 1 2 3. 2 0 5. 2 1 7 3.

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乘法公式

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  1. 乘法公式 國中數學 第3冊

  2. （a + b）（c + d）＝ ac + bc + ad + bd a ＋b a b ac ( a + b ) × c bc c c ＋d ad bd ( a + b ) × d d （a + b）×（c + d） =（a + b）× c +（a + b）× d = ac + bc + ad + bd

  3. 4 1 × 5 3 1 2 3 2 0 5 2 1 7 3 （a + b）（c + d）＝ ac + bc + ad + bd 41 ×53 =（40 + 1）×（50 + 3） 41 × 3 41 × 50 = 40 × 50 + 1 × 50 + 40 × 3 + 1 × 3 = 2000 + 50 + 120 + 3 = 2173

  4. （a + b）（c + d）＝ ac + bc + ad + bd x ＋2 a = x，b = 2，c = x，d = 3 x 2 x2 2 x x （x + 2）（x + 3） x + 3 = x2 + 2x + 3x + 6 3 x 6 3 = x2 + 5x +6

  5. （a + b）2 ＝ a2 + 2ab + b2 a + b a b a2 ab （a + b）2 a ＝（a + b）×（a + b） a + b ＝a2 + ab +ab + b2 ab b2 b ＝a2 + 2ab + b2

  6. （a + b）2＝ a2 + 2ab + b2 10.6 2 hint （ a + b ）2＝a2 + 2 ×a ×b + b2 ＝（10 + 0.6）2＝102 + 2 × 10 × 0.6 + 0.62 = 100 + 12 + 0.36 = 112.36

  7. （a – b）2＝ a2 – ab + b2 – ab （a – b）2＝ a2 – ab + b2 – ab ＝ a2 – 2ab + b2 a a a b b2 b （a – b）2 a b a2 a a – b b a – b

  8. （a – b）2＝ a2 – 2ab + b2 hint hint 9.92 =（10 – 0.1）2 982 =（100 – 2）2 a2 – 2 ×a ×b + b2 a2 – 2 ×a ×b + b2 = 1002 – 2 × 100 × 2 + 4 = 102 – 2 × 10 × 0.1 +（0.1）2 = 100 – 2 + 0.01 = 10000 – 400 + 4 = 98.01 = 9604

  9. （a + b）（a – b）= a2 – b2 a a b b b2 b a a – b a + b

  10. （a + b）（a – b）= a2 – b2 2502 × 2498 100.3 × 99.7 =（2500 + 2）×（2500 – 2） =（100 + 0.3）×（100 – 0.3） = 25002 – 22 = 1002 – 0.32 = 6250000 – 4 = 10000 – 0.09 = 6249996 = 9999.91

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