灵鹊做题网这几道因式分解题怎么解啊
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/05/02 16:54:50
这几道因式分解题怎么解啊
1.（c^2-b^2+d^2+a^2)-4(ab-cd)^2
2.x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
3.m^4+m^2-2mn-n^2+1
4.(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2+c^2+d^2)
(注：^号后面的数代表字母的次数,
1.（c^2-b^2+d^2+a^2)-4(ab-cd)^2
2.x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
3.m^4+m^2-2mn-n^2+1
4.(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2+c^2+d^2)
(注：^号后面的数代表字母的次数,
1.原式=（1+2b）*（1-2b)a^2+8bcd*a+c^2+d^2-4c^2d^2-b^2末项不能分解,而首项末项不能组成8bcda,因此可以判定本题不能分解.
2.原式 =x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
=ax^3+x^3-ayx^2+byx^2+axy^2-bxy^2+by^3+y^3
=ax(x^2-xy+y^2)+by(x^2-xy+y^2)+(x+y)(x^2-xy+y^2)
=〔(a+1)x+(b+1)y〕(x^2-xy+y^2)
=（ax+x+by+y)(x^2-xy+y^2)
3.原式=(m^4+2m^2+1)-(m^2+2mn+n^2)
=(m^2+1)^2-(m+n)^2
=(m^2+1+m+n)(m^2+1-m-n)
4.题目出错了,最后的括号内应为-c^2-d^2
原式=(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-c^2-d^2)
=(a^2-d^2)(ab+cd+ac+bd)+(c^2-b^2)(ab+cd-ac-bd)
=(a-d)(a+d)(a+d)(b+c)+(c-b)(c+b)(a-d)(b-c)
=(a-d)((b+c)[(a+d)^2-(b-c)^2]
=(a-d)(b+c)(a+d+b-c)(a+d-b+c).
否则后来不能合并同类项.
如果LZ还需更难的因式分解,试分解该题6x^4+18mx^3-6x^3y+30x^2yz-42x^2y^2+6mx^2y-6x^2mz-6x^2z+12x^2m^2+5px^3+5yx^3+15pm-5py+25pyz+25y^2z-30py^2-30y^3+5mpy+5my^2-5pmz-5myz-5pz^2-5yz^2+10pm^2+10m^2y+10yzx^2+30myzx-10xy^2z+50y^2z^2-60y^3z+10my^2z-
10myz^2-10yz^3+20m^2yz-18my^2x+6xy^3-30y^3z+36y^4-6my^3+6my^2z+6y^2z^2-12y^2m^2+10x^2zp+30zpmx-10zpyx
+50yz^2p-60y^2zp-2zpmy-10z^2pm-10z^3p-12x^2zp-36mypx+12y^2px-60y^2pz+72y^3p-12my^2p+12ypmz+12ypz^2-24m^2yp-6p^2x^2-18mxp^2+6xyp^2-30yzp^2+36p^2y^2-6myp^2+6p^2mz+6p^2z^2-12P^2m^2+24x^2z^2+72mz^2x-24yz^2+120yz^3-144y^2z^2+24myz^2-24mz^3+24z^4+48m^2z^2
答案为=(2x+3y+4z+3p)(3x-2y+6z-2p)(x+2y-z+m)(x-3y+z+2m)
2.原式 =x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
=ax^3+x^3-ayx^2+byx^2+axy^2-bxy^2+by^3+y^3
=ax(x^2-xy+y^2)+by(x^2-xy+y^2)+(x+y)(x^2-xy+y^2)
=〔(a+1)x+(b+1)y〕(x^2-xy+y^2)
=（ax+x+by+y)(x^2-xy+y^2)
3.原式=(m^4+2m^2+1)-(m^2+2mn+n^2)
=(m^2+1)^2-(m+n)^2
=(m^2+1+m+n)(m^2+1-m-n)
4.题目出错了,最后的括号内应为-c^2-d^2
原式=(ab+cd)(a^2-b^2+c^2-d^2)+(ac+bd)(a^2+b^2-c^2-d^2)
=(a^2-d^2)(ab+cd+ac+bd)+(c^2-b^2)(ab+cd-ac-bd)
=(a-d)(a+d)(a+d)(b+c)+(c-b)(c+b)(a-d)(b-c)
=(a-d)((b+c)[(a+d)^2-(b-c)^2]
=(a-d)(b+c)(a+d+b-c)(a+d-b+c).
否则后来不能合并同类项.
如果LZ还需更难的因式分解,试分解该题6x^4+18mx^3-6x^3y+30x^2yz-42x^2y^2+6mx^2y-6x^2mz-6x^2z+12x^2m^2+5px^3+5yx^3+15pm-5py+25pyz+25y^2z-30py^2-30y^3+5mpy+5my^2-5pmz-5myz-5pz^2-5yz^2+10pm^2+10m^2y+10yzx^2+30myzx-10xy^2z+50y^2z^2-60y^3z+10my^2z-
10myz^2-10yz^3+20m^2yz-18my^2x+6xy^3-30y^3z+36y^4-6my^3+6my^2z+6y^2z^2-12y^2m^2+10x^2zp+30zpmx-10zpyx
+50yz^2p-60y^2zp-2zpmy-10z^2pm-10z^3p-12x^2zp-36mypx+12y^2px-60y^2pz+72y^3p-12my^2p+12ypmz+12ypz^2-24m^2yp-6p^2x^2-18mxp^2+6xyp^2-30yzp^2+36p^2y^2-6myp^2+6p^2mz+6p^2z^2-12P^2m^2+24x^2z^2+72mz^2x-24yz^2+120yz^3-144y^2z^2+24myz^2-24mz^3+24z^4+48m^2z^2
答案为=(2x+3y+4z+3p)(3x-2y+6z-2p)(x+2y-z+m)(x-3y+z+2m)