Chapter 1 - Introduction to Algebraic Expressions - 1.8 Exponential Notation and Order of Operations - 1.8 Exercise Set - Page 67: 89

$-t^3+4t$

Using $a(b+c)=ab+ac$ or the Distributive Property and then combining like terms, the given expression, $ 5t^3+t+3(t-2t^3) $, simplifies to \begin{array}{l}\require{cancel} 5t^3+t+3(t)+3(-2t^3) \\\\= 5t^3+t+3t-6t^3 \\\\= (5t^3-6t^3)+(t+3t) \\\\= -t^3+4t .\end{array}