Question

.Разложите на множителиp^3-t^327-p^38t^3+18p^3+125t^3^степень

Answer 1

по формулам $a^3+b^3=(a+b)(a^2-ab+b^2) \\ \\ a^3-b^3=(a-b)(a^2+ab+b^2)$

 все разлаживаетcя как

 

$a^3-t^3=(a-t)(a^2+at+t^2) \\ \\ \\ 27-p^3=3^3-p^3= \\ \\ = (3-p)(3^2+3*p+p^2)=(3-p)(9-3p+p^2) \\ \\ \\ 8t^3+1= (2t)^3+1^3= \\ \\ = (2t+1)((2t)^2-1*2t+1^2)=(2t+1)(4t^2-2t+1) \\ \\ \\ 8p^3+125t^3=(2p)^3+(5t)^3= \\ \\ = (2p+5t)((2p)^2-2p*5t+(5t)^2) = \\ \\ = (2p+5t)(4p^2-10pt+25t^2)$