因式分解:(1)(x+1)(x+3)(x+5)(x+7)+15(2)6x²-6y²+5xy-4x+7
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/14 02:28:18
因式分解:
(1)
(x+1)(x+3)(x+5)(x+7)+15
(2)
6x²-6y²+5xy-4x+7y-2
(1)
(x+1)(x+3)(x+5)(x+7)+15
(2)
6x²-6y²+5xy-4x+7y-2
1.(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x+7)[(x^2+8x+7)+8]+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=[(x^2+8x+7)+3][(x^2+8x+7)+5]
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
2.6x²-6y²+5xy-4x+7y-2
=(3X-2Y)(2X+3Y)-(4X-7Y)-2
=(3X-2Y+1)(2X+3Y-2)
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x+7)[(x^2+8x+7)+8]+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=[(x^2+8x+7)+3][(x^2+8x+7)+5]
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
2.6x²-6y²+5xy-4x+7y-2
=(3X-2Y)(2X+3Y)-(4X-7Y)-2
=(3X-2Y+1)(2X+3Y-2)
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