Question

Add or subtract. $$\left(4 t^{2}+5 t+2\right)-\left(t^{2}-3 t-8\right)$$

Short answer

The solution to the subtraction of these two trinomials is \(3t^2 + 8t + 10\).

Step-by-step solution

Rewrite the Equation

It's necessary to rewrite the equation, removing the parentheses. Remember that a minus sign before a parenthesis means to change the sign of each term inside the parenthesis. The equation then looks like this: \(4t^2+5t+2 - t^2 + 3t + 8\)

Combine Like Terms

Then proceed by adding together the like terms. The like terms are those which have the same variable raised to the same power. Here, these are \(4t^2 - t^2\), \(5t + 3t\) and \(2 + 8\). The addition of these terms results in the combined expression: \(3t^2 + 8t + 10\)

Write down the final result

The final result of this polynomial subtraction is: \(3t^2 + 8t + 10\)