7道有难度的分解因式题一、拆项、添项法:1、x^3-9x+82、x^9+x^6+x^3-33、(m^2-1)(n^2-1)+4mn4、a^3*b-ab^3+a^2+b^2+1二、换元法:5、6x^4+7x^3-36x^2-7x+66、(x^2+3x+2)(4x^2+8x+3)-907、(x^2+xy+y^2)-4xy(x^2+y^2)#只需答出一
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![7道有难度的分解因式题一、拆项、添项法:1、x^3-9x+82、x^9+x^6+x^3-33、(m^2-1)(n^2-1)+4mn4、a^3*b-ab^3+a^2+b^2+1二、换元法:5、6x^4+7x^3-36x^2-7x+66、(x^2+3x+2)(4x^2+8x+3)-907、(x^2+xy+y^2)-4xy(x^2+y^2)#只需答出一](/uploads/image/z/13766025-57-5.jpg?t=7%E9%81%93%E6%9C%89%E9%9A%BE%E5%BA%A6%E7%9A%84%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%E9%A2%98%E4%B8%80%E3%80%81%E6%8B%86%E9%A1%B9%E3%80%81%E6%B7%BB%E9%A1%B9%E6%B3%95%EF%BC%9A1%E3%80%81x%5E3-9x%2B82%E3%80%81x%5E9%2Bx%5E6%2Bx%5E3-33%E3%80%81%28m%5E2-1%29%28n%5E2-1%29%2B4mn4%E3%80%81a%5E3%2Ab-ab%5E3%2Ba%5E2%2Bb%5E2%2B1%E4%BA%8C%E3%80%81%E6%8D%A2%E5%85%83%E6%B3%95%EF%BC%9A5%E3%80%816x%5E4%2B7x%5E3-36x%5E2-7x%2B66%E3%80%81%28x%5E2%2B3x%2B2%29%284x%5E2%2B8x%2B3%29-907%E3%80%81%28x%5E2%2Bxy%2By%5E2%29-4xy%28x%5E2%2By%5E2%29%23%E5%8F%AA%E9%9C%80%E7%AD%94%E5%87%BA%E4%B8%80)
7道有难度的分解因式题一、拆项、添项法:1、x^3-9x+82、x^9+x^6+x^3-33、(m^2-1)(n^2-1)+4mn4、a^3*b-ab^3+a^2+b^2+1二、换元法:5、6x^4+7x^3-36x^2-7x+66、(x^2+3x+2)(4x^2+8x+3)-907、(x^2+xy+y^2)-4xy(x^2+y^2)#只需答出一
7道有难度的分解因式题
一、拆项、添项法:
1、x^3-9x+8
2、x^9+x^6+x^3-3
3、(m^2-1)(n^2-1)+4mn
4、a^3*b-ab^3+a^2+b^2+1
二、换元法:
5、6x^4+7x^3-36x^2-7x+6
6、(x^2+3x+2)(4x^2+8x+3)-90
7、(x^2+xy+y^2)-4xy(x^2+y^2)
#只需答出一道或几道即可,正确最多的回答追加50分!
7道有难度的分解因式题一、拆项、添项法:1、x^3-9x+82、x^9+x^6+x^3-33、(m^2-1)(n^2-1)+4mn4、a^3*b-ab^3+a^2+b^2+1二、换元法:5、6x^4+7x^3-36x^2-7x+66、(x^2+3x+2)(4x^2+8x+3)-907、(x^2+xy+y^2)-4xy(x^2+y^2)#只需答出一
1、x^3-9x+8=(x-1)(x^2-x+8)
2、x^9+x^6+x^3-3=(x^9-1)+(x^6-1)+(x^3-1)
=(x^3-1)(x^6+x^3+1+x^3+1+1)
=(x^3-1)(x^6+2x^3+3)
3、(m^2-1)(n^2-1)+4mn=m^2n^2-m^2-n^2+1+4mn
=(mn)^2+2mn+1-(m^2+n^2-2mn)
=(mn+1)^2-(m-n)^2
=(mn+m-n+1)(mn-m+n+1)
4、a^3*b-ab^3+a^2+b^2+1
=(ab+b^2+1)(a^2-ab+1)
二、换元法:
5、6x^4+7x^3-36x^2-7x+6
=x^2(6(x^2+1/x^2)+7(x-1/x)-36)
=x^2(6(x-1/x)^2+7(x-1/x)-24)
=x^2(2x-2/x-3)(3x-3/x+8)
=(2x^2-3x-2)(3x^2+8x-3)
=(2x+1)(x-2)(3x+1)(x-3)
6、(x^2+3x+2)(4x^2+8x+3)-90
=(x+1)(x+2)(2x+1)(2x+3)-90
=(2x^2+5x+2)(2x^2+5x+3)-90 (将2x^2+5x+2看作整体)
=(2x^2+5x+2)^2+(2x^2+5x+2)-90
=(2x^2+5x+2-9)(2x^2+5x+2+10)
=(x-1)(2x+7)(2x^2+5x+12)
7、(x^2+xy+y^2)-4xy(x^2+y^2)暂时不会做.
1、x^3-9x+8 = (x^3-1)-9x+9 = (x-1)(x^2+x+1)-9(x-1) = (x-1)(x^2+x-8)
2、x^9+x^6+x^3-3 = (x^9-1)+(x^6-1)+(x^3-1) = (x^3-1)(x^6+x^3+1)+(x^2-1)(x^4+x^2+1)+(x-1)(x^2+x+1) =(x-1)(x^2+x+1)(x^6+x^3+1)+(x-1)...
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1、x^3-9x+8 = (x^3-1)-9x+9 = (x-1)(x^2+x+1)-9(x-1) = (x-1)(x^2+x-8)
2、x^9+x^6+x^3-3 = (x^9-1)+(x^6-1)+(x^3-1) = (x^3-1)(x^6+x^3+1)+(x^2-1)(x^4+x^2+1)+(x-1)(x^2+x+1) =(x-1)(x^2+x+1)(x^6+x^3+1)+(x-1)(x+1)(x^4+x^2+1)+(x-1)(x^2+x+1)
=(x-1)[(x^2+x+1)(x^6+x^3+1)+(x+1)(x^4+x^2+1)+(x^2+x+1)]
3、(m^2-1)(n^2-1)+4mn =m^2n^2-m^2-n^2+1+4mn
= (m^2n^2+1+2mn)-(m^2+n^2-2mn)
=(mn+1)^2-(m-n)^2 = (mn+1+m-n)(mn+1-m+n)
6、(x^2+3x+2)(4x^2+8x+3)-90
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=4x^4+20x^3+35x^2+25x-84 =(4x^4-4)+(20x^3-20)+(35x^2-35)+(25x-25)
=4(x-1)(x+1)(x^2+1)+20(x-1)(x^2+x+1)+35(x-1)(x+1)+25(x-1)
=(x-1){4(x+1)(x^2+1)+20(x^2+x+1)+35(x+1)+25]
后面的自己做吧,打得很辛苦啊
收起
1
(x-1)(x^2+x-8)
3
(mn-m+n+1)(mn+m-n+1)
1: =x^3-1-9x+9=(x-1)*(x^2+x+1)-9*(x-1)=(x-1)*(x^2+x-8)
2: =x^3^3-1+x^3^2-1+x^3-1=(x^3-1)(x^3^2+x^3+1)+(x^3-1)(x^3+1)+(x^3-1)=(x^3-1)(x^3^2+x^3+1+x^3+1+1)=(x-1)(x^2+x+1)(x^6+2x^3+3)
3: =(mn)^2-...
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1: =x^3-1-9x+9=(x-1)*(x^2+x+1)-9*(x-1)=(x-1)*(x^2+x-8)
2: =x^3^3-1+x^3^2-1+x^3-1=(x^3-1)(x^3^2+x^3+1)+(x^3-1)(x^3+1)+(x^3-1)=(x^3-1)(x^3^2+x^3+1+x^3+1+1)=(x-1)(x^2+x+1)(x^6+2x^3+3)
3: =(mn)^2-m^2-n^2+1+2mn+2mn=(mn+1)^2-(m-n)^2=(mn+m-n+1)(mn-m+n+1)
4: =
5: =x^2(6(x^2+1/x^2)+7(x-1/x)-36)=x^2(6(x-1/x)^2+7(x-1/x)- 24)=x^2(2x-2/x-3)(3x-3/x+8)=(2x^2-3x-2)(3x^2+8x-3)= (2x+1)(x-2)(3x+1)(x-3)
别的正在做
收起
x^3-9x+8 =x^3+x^2-8x-x^2-x+8=(x-1)(x^2+x-8)