(1)6x n+1 -14x n +8x n-1 (2)(x+1)(x+2)(x+3)(x+4)+1 (3)(1-a 2
来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/05/24 08:18:37
(1)6x n+1 -14x n +8x n-1 (2)(x+1)(x+2)(x+3)(x+4)+1 (3)(1-a 2 )(1-b 2 )-4ab (4)8a 3 -b 3 (5)3x 2 +5xy-2y 2 +x+9y-4 (6)2x 2 +xy-y 2 -4x+5y-6 (7)x 2 +x-(a 2 -a)
(1)6x n+1 -14x n +8x n-1=2x^(n-1)[3x^2-7x+4]=2x^(n-1)(x-1)(3x-4) (2)(x+1)(x+2)(x+3)(x+4)+1=[(x+1)(x+4)][(x+2)(x+3)]+1 =[(x^2+5x)+4][(x^2+5x)+6]+1 =(x^2+5x)^2+10(x^2+5x)+25 =(x^2+5x+5)^2 (3)(1-a 2 )(1-b 2 )-4ab=(ab)^2-(a^2+b^2)+1-4ab=[(ab)^2-2ab+1]-[a^2+b^2+2ab] =(ab-1)^2-(a+b)^2 =(ab-1+a+b)(ab-1-a-b) (4)8a^3-b^3=(2a)^3-b^3=(2a-b)(4a^2+2ab+b^2) (5)3x^2+5xy-2y^2+x+9y-4=(3x^2+5xy-2y^2)+x+9y-4 =(3x-y)(x+2y)+4(x+2y)-(3x-y)-4 =(3x-y+4)(x+2y-1) (6)2x^2+xy-y^2-4x+5y-6=(2x^2+xy-y^2)-4x+5y-6=(x+y)(2x-y)+2(x+y)-3(2x-y)-6 =[(x+y)-3][(2x-y)+2]=(x+y-3)(2x-y+2) (7)x^2+x-(a^2-a)=(x^2-a^2)+(x+a)=(x-a)(x+a)+(x+a)=(x+a)(x-a+1)
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