Phân tích đa thức thành nhân tử(dạng đối xứng vòng quanh).
1)(a-b)(b-c)(a-c)+(a+b)(b+c)(a-c)+(a+b)(a+c)(c-b)
2)-(mab+n)(a-b)-(mbc+n)(b-c)-(mca+n)(c-a)
3)(aut+n)(u-t)+(auv+n)(v-u)+(atv+n)(t-v)
4)bc(a+d)(b-c)+ac(b+d)(c-a)+ab(c+d)(a-b)
Phân tích đa thức thành nhân tử(dạng đối xứng vòng quanh). 1)(a-b)(b-c)(a-c)+(a+b)(b+c)(a-c)+(a+b)(a+c)(c-b) 2)-(mab+n)(a-b)-(mbc+n)(b-c)-(mca+n)(c-a)
By Valerie
1)(a-b)(b-c)(a-c)+(a+b)(b+c)(a-c)+(a+b)(a+c)(c-b)
=a²b-ab²-a²c+abc-abc+b²c+ac²-bc²+ a²b+ab²+a²c+abc-abc-b²c-ac²-bc² -a²b-ab²+a²c+abc-abc-b²c+ac²+bc²
=a²b-ab²+a²c-b²c+ac²-bc²-abc+abc
=a(ab-b²+ac-bc)+c(ab-b²+ac-bc)
=[(ab-b²)+(ac-bc)](a+c)
=[b(a-b)+c(a-b)](a+c)
=(a-b)(b+c)(a+c)
2)-(mab+n)(a-b)-(mbc+n)(b-c)-(mca+n)(c-a)
=-ma²b+mab²-na+nb-mb²c+mbc²-nb+nc-mc²a+mca²-nc+na
=-m[a²b-ab²+b²c-bc²+c²a-ca²+abc-abc]
=-m[a(ab-b²+bc-ac)-c(ab+b²+bc-ac)]
=-m{(a-c)[ab-b²+bc-ac]}
=-m(a-b)(b+c)(a-c)
3)(aut+n)(u-t)+(auv+n)(v-u)+(atv+n)(t-v)
{Tương tự với (2)}
=a(t-v)(v+u)(u-t)
4)bc(a+d)(b-c)+ac(b+d)(c-a)+ab(c+d)(a-b)
=ab²c-abc²+b²cd-bc²d+abc²-a²bc+ac²d-a²cd+a²bc-ab²c+a²bd-ab²d
=b²cd-bc²d+ac²d-a²cd+a²bd-ab²d
=d[b²c-bc²+ac²-a²c+a²b-ab²]
=d[(b²c-bc²+ac²-abc)+(-a²c+a²b-ab²+abc)]
=d[c(b²-bc+ac-ab)-a(ac-ab+b²-bc)]
=d[(c-a)(b²-bc+ac-ab)]
=d(c-a)[(b²-bc)+(ac-ab)]
=d(c-a)[b(b-c)-a(b-c)]
=d(c-a)(b-c)(b-a)
1)(a-b)(b-c)(a-c)+(a+b)(b+c)(a-c)+(a+b)(a+c)(c-b)
=a²b-ab²-a²c+abc-abc+b²c+ac²-bc²+ a²b+ab²+a²c+abc-abc-b²c-ac²-bc² -a²b-ab²+a²c+abc-abc-b²c+ac²+bc²
=a²b-ab²+a²c-b²c+ac²-bc²-abc+abc
=a(ab-b²+ac-bc)+c(ab-b²+ac-bc)
=[(ab-b²)+(ac-bc)](a+c)
=(a-b)(b+c)(a+c)
2)-(mab+n)(a-b)-(mbc+n)(b-c)-(mca+n)(c-a)
=-ma²b+mab²-na+nb-mb²c+mbc²-nb+nc-mc²a+mca²-nc+na
=-m[a²b-ab²+b²c-bc²+c²a-ca²+abc-abc]
=-m[a(ab-b²+bc-ac)-c(ab+b²+bc-ac)]
=-m(a-b)(b+c)(a-c)
3)(aut+n)(u-t)+(auv+n)(v-u)+(atv+n)(t-v)
=au²t-aut²+nu-nt+auv²-au²v+nv-nu+at²v-atv²+nt-nv
=au²t-aut²+auv²-au²v+at²v-atv²
=a(u²t-ut²+uv²-u²v+t²v-tv²)
=a(u²t-ut²+uv²-u²v+t²v-tv²+tuv-tuv)
=a[u(ut-t²+tv-uv)-v(-uv²-t²+tv+ut)]
=a(t-v)(v+u)(u-t)
4)bc(a+d)(b-c)+ac(b+d)(c-a)+ab(c+d)(a-b)
=ab²c-abc²+b²cd-bc²d+abc²-a²bc+ac²d-a²cd+a²bc-ab²c+a²bd-ab²d
=b²cd-bc²d+ac²d-a²cd+a²bd-ab²d
=d[b²c-bc²+ac²-a²c+a²b-ab²+abc-abc]
=d[c(b²-bc+ac-ab)-a(ac-ab+b²-bc)]
=d[(c-a)(b²-bc+ac-ab)]
=d(c-a)[b(b-c)-a(b-c)]
=d(c-a)(b-c)(b-a)
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