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國中數學問題，乘法公式?
1.估算2009*(-(2009/2008))最接近哪一數?(為甚麼最接近-2010)2.算式743*369-741*370之值為何是-33.555^2-222^2=333^2+a*111，a=?
1) 2009*[-(2009/2008)] -2009 = (2008+1) [ ---------- ] 2008 -2009-2009 = (2008) [ ---------- ] + 1 [ ---------- ] - - - - - - - - - → 《乘法公式: (a+b) c = ac + bc》 2008 2008 -2009 = - 2009 + ----------- 2008 ≒ -2009 - 1 ≒ -2010 2) 743*369-741*370 = 743(370-1) - 741(370) ^^^^^^^^^^ = 743(370) - 741(370) - 743 →《乘法公式: a(b-c) = ab - ac》,即 743(370-1) = 743(370)-743 ^^^^^^^^ ^^^^^ = (743 - 741) (370) - 743 = 2 (370) - 743 = 740 - 743 = -3 3) 5552 - 2222 = 3332 + a*111 5552 - 2222 - 3332 = 111 a 1112 (52 - 22 - 32) = 111 a 111 (25 - 4 - 9) = a ∴ a = 111 (12) = 1332
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