Question

Use a vertical format or a horizontal format to add or subtract. $$\left(21 t^{4}-3 t^{2}+43\right)-\left(19 t^{3}+33 t-58\right)$$

Short answer

The final result after subtracting the two polynomials is \(21 t^{4} - 19 t^{3} - 3 t^{2} - 33 t + 101\)

Step-by-step solution

Distribute the Minus Sign

This step involves distributing the negative sign to every term in the second set of brackets. The expression becomes: \(21 t^{4} - 3 t^{2} + 43 - 19 t^{3} - 33 t + 58 \)

Rearrange the Terms

Rearrange the terms from highest order to lowest order to make the next step easier. \(21 t^{4} - 19 t^{3} - 3 t^{2} - 33 t + 43 + 58\)

Combine Like Terms

Combine the like terms to simplify the expression, resulting in the answer. Like terms are those that involve the same power of \( t \). Here, '43' and '58' are like terms. When combined, the final expression becomes: \(21 t^{4} - 19 t^{3} - 3 t^{2} - 33 t + 101\)