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標題:

1.(3x+5)(2x-3)=6x^2+x-15

發問:

1.(3x+5)(2x-3)=6x^2+x-15 2.找出未知數 (2x+1)(x-3)=Ax^2+Bx+C

最佳解答:

1. (3x+5)(2x-3)=6x^2+x-15 LHS = (3x+5)(2x-3) = 6x^2-9x+10x-15 = 6x^2+x-15 = RHS therefore, (3x+5)(2x-3) 三 6x^2+x-15 (三 = 全等) 2. 找出未知數 (2x+1)(x-3)=Ax^2+Bx+C LHS = (2x+1)(x-3) = 2x^2-6x+x-3 = 2x^2-5x-3 所以A = 2, B = -5, C = -3 (如果要用(1)答案做) LHS = [(3x+5)-(x+4)] [(2x-3)-x)] = (3x+5)(x-3) - x(3x+5) - (x+4)(2x-3) + x(x+4) = (3x+5)(x-3) - x(3x+5-x-4) - (2x^2-3x+8x-12) = (3x+5)(x-3) - x(2x+1) - (2x^2+5x-12) = 6x^2+x-15 - 2x^2-x - 2x^2-5x+12..........(把(1)答案套入) = (6-2-2)x^2 + (1-1-5)x + (12-15) = 2x^2+5x-3 所以A = 2, B = -5, C = -3

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其他解答:

1. (3x+5)(2x-3)=6x^2+x-15 6x^2-9x+10x-15=6x^2+x-15 6x^2+x-15=6x^2+x-15 0=0 it is an identity 2. (2x+1)(x-3)=2x^2-6x+x-3 =2x^2-5x+3 By comparing the like terms, A=2 B=-5 C=3
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