The simplified expression is [tex]15 x^{6}+20 x^{5}+10 x^{4}[/tex]Explanation:Given that the expression is [tex]-5 x^{4}\left(-3 x^{2}-4 x-2\right)[/tex]We need to determine the simplify the expression.Let us multiply each term within the parenthesis by the term [tex]-5 x^{4}[/tex]Thus, we have,[tex]\left(-5 x^{4}\right)\left(-3 x^{2}\right)+\left(-5 x^{4}\right)(-4 x)+\left(-5 x^{4}\right)(-2)[/tex]Applying the rule, [tex](-a)(-b)=a b[/tex] in the above expression, we get,[tex]\left(5 x^{4}\right)\left(3 x^{2}\right)+\left(5 x^{4}\right)(4 x)+\left(5 x^{4}\right)(2)[/tex]Let us simplify by multiplying the terms.Thus, we get,[tex]15 x^{6}+20 x^{5}+10 x^{4}[/tex]Hence, the simplified expression is [tex]15 x^{6}+20 x^{5}+10 x^{4}[/tex]