Question

Разложи на множители v3−t2v−tv2+t3.


 

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Answer 1

$v^3-t^2v-tv^2+t^3=(v^3-tv^2)+(t^3-t^2v)=\\\\=v^2\, (v-t)-t^2\, (v-t)=(v-t)(v^2-t^2)=(v-t)(v-t)(v+t)=\\\\=(v-t)^2(v+t)$