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