Answer:
[tex]\left(-t^4-5t^3-10t^2\right)+\left(9t^3+3t^2-1\right)=-t^4+4t^3-7t^2-1[/tex]
Step-by-step explanation:
Given the expression
[tex]\left(-t^4\:-5t^3\:-10t^2\:\right)+\left(9t^3\:+3t^2\:-1\right)[/tex]
Remove parentheses: (a)=a
[tex]=-t^4-5t^3-10t^2+9t^3+3t^2-1[/tex]
Group like terms
[tex]=-t^4-5t^3+9t^3-10t^2+3t^2-1[/tex]
Add similar elements
[tex]=-t^4-5t^3+9t^3-7t^2-1[/tex] ∵ [tex]-10t^2+3t^2=-7t^2[/tex]
Add similar elements
[tex]=-t^4+4t^3-7t^2-1[/tex] ∵ [tex]-5t^3+9t^3=4t^3[/tex]
Thus, the equivalent expression in simplified form:
[tex]\left(-t^4-5t^3-10t^2\right)+\left(9t^3+3t^2-1\right)=-t^4+4t^3-7t^2-1[/tex]
