因式分解:1.2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²2.(x+1)(x+3)(x+5)(x+7)+15看答案看了半天也没搞懂,唉,我初高中脱节了
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/10 09:38:49
![因式分解:1.2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²2.(x+1)(x+3)(x+5)(x+7)+15看答案看了半天也没搞懂,唉,我初高中脱节了](/uploads/image/z/8524560-48-0.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9A1.2%EF%BC%88x%26%23178%3B%2B6x%2B1%EF%BC%89%26%23178%3B%2B5%EF%BC%88x%26%23178%3B%2B1%EF%BC%89%EF%BC%88x%26%23178%3B%2B6x%2B1%EF%BC%89%2B2%EF%BC%88x%26%23178%3B%2B1%EF%BC%89%26%23178%3B2.%EF%BC%88x%2B1%EF%BC%89%EF%BC%88x%2B3%EF%BC%89%EF%BC%88x%2B5%EF%BC%89%EF%BC%88x%2B7%EF%BC%89%2B15%E7%9C%8B%E7%AD%94%E6%A1%88%E7%9C%8B%E4%BA%86%E5%8D%8A%E5%A4%A9%E4%B9%9F%E6%B2%A1%E6%90%9E%E6%87%82%2C%E5%94%89%2C%E6%88%91%E5%88%9D%E9%AB%98%E4%B8%AD%E8%84%B1%E8%8A%82%E4%BA%86)
因式分解:1.2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²2.(x+1)(x+3)(x+5)(x+7)+15看答案看了半天也没搞懂,唉,我初高中脱节了
因式分解:
1.2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²
2.(x+1)(x+3)(x+5)(x+7)+15
看答案看了半天也没搞懂,唉,我初高中脱节了
因式分解:1.2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²2.(x+1)(x+3)(x+5)(x+7)+15看答案看了半天也没搞懂,唉,我初高中脱节了
第一题(2(x²+6x+1)+(x²+1))*((x²+6x+1)+2(x²+1))
第二题 ((x+1)(x+7))((x+3)(x+5))+15
=(x²+8x+7)(x²+8x+15)+15
=(x²+8x+7)(x²+8x+15)+8(x²+8x+15)-8(x²+8x+15)+15
=(x²+8x+15)²-8(x²+8x+15)+15
=(x²+8x+15-3)(x²+8x+15-5)
1
2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²
=(2(x²+6x+1)+(x²+1))((x²+6x+1)+2(x²+1))
2
(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+...
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1
2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²
=(2(x²+6x+1)+(x²+1))((x²+6x+1)+2(x²+1))
2
(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)
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太简单了,先合并脱括号再分解就行了
1. 2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²
=[(x²+6x+1)+2(x²+1)]*[2(x²+6x+1)+(x²+1)]
=(3x²+6x+3)*(3x²+12x+3)
=3(x²+2x+1)*3(x...
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1. 2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²
=[(x²+6x+1)+2(x²+1)]*[2(x²+6x+1)+(x²+1)]
=(3x²+6x+3)*(3x²+12x+3)
=3(x²+2x+1)*3(x²+4x+1)
=3(x+1)²3*(x²+4x+1)
=9(x+1)²(x²+4x+1)
2. (x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)]*[(x+3)(x+5)]+15
=[(x²+8x)+7]*[(x²+8x)+15]+15
=(x²+8x)²+22(x²+8x)+120
=(x²+8x+10)*(x²+8x+12)
=(x²+8x+10)*(x+2)*(x+6)
其实,这两道题就是障眼法,你只要把第一题的(x²+6x+1)看成是a,(x²+1)看成是b,那题目就变成了2a²+5ab+2b²,十字相乘一下子就出来了。第二题也是类似的想法,就不赘述了。
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