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標題:

f.3因式分解 急急急急!!!!

發問:

(A) 16-x^2-y^2+2xy (B) 4a^2-9B^2+4a+1 (C) x^2+2xy+y^2-x-y (D) (2x+1)(x+7)-6x 步驟+答案

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您好，我是 lop，高興能解答您的問題。 (A) 16 - x^2 - y^2 + 2xy = ( xy - x^2 ) - ( y^2 - xy ) + 16 = x(y-x) - y(y-x) + 16 = (x-y)(y-x) + 16 = -(y-x)^2 + 16 = 16 - (y-x)^2 = 4^2 - (y-x)^2 = [4+(y-x)][4-(y-x)]註(1) = (4-x+y)(4+x-y) (B) 4a^2-9B^2+4a+1 = ( 4a^2 + 4a + 1 ) - 9B^2 = ( 4a^2 + 2a ) + ( 2a + 1 ) - (3B)^2 = 2a(2a+1) + 1(2a+1) - (3B)^2 = (2a+1)(2a+1) - (3B)^2 = (2a+1)^2 - (3B)^2 = (2a+3B+1)(2a-3B+1)註(1) (C) x^2+2xy+y^2-x-y = ( x^2 + xy ) + ( xy + y^2 ) - ( x + y ) = x(x+y) + y(x+y) - 1(x+y) = (x+y-1)(x+y) (D) (2x+1)(x+7)-6x = 2x^2 + 15x + 7 - 6x = 2x^2 + 9x + 7 = ( 2x^2 + 2x ) + ( 7x + 7 ) = 2x(x+1) + 7(x+1) = (x+1)(2x+7) 註： (1) 緊記公式 x^2 - y^2 = (x+y)(x-y)

其他解答:

(A) 16-x^2-y^2+2xy =-x^2+2xy-y^2+16 =-(x^2-2xy+y^2)+16 =-(x-y)^2+16 =-[(x-y)+4][(x-y)-4] =-(x-y+4)(x-y-4) (B) 4a^2-9B^2+4a+1 =4a^2+4a+1-9B^2 =(2a+1)^2-9B^2 =[(2a+1)-3B][(2a+1)+3B] =(2a-3b+1)(2a+3b+1) (C) x^2+2xy+y^2-x-y =(x+y)^2-(x+y) =(x+y)(x+y+1) (D) (2x+1)(x+7)-6x =2x^2+14x+x+7-6x =2x^2+9x+7 =(2x+7)(x+1)