Question

subtract.\\((9d^{3} + 3d^{2} + 5d + 8) - (8d^{3} + 2d^{2} + d + 1)\\)

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we need to distribute the negative sign to each term in the second polynomial. So we have:
\(9d^{3}+3d^{2}+5d + 8-8d^{3}-2d^{2}-d - 1\)

Step2: Combine like terms for \(d^{3}\) terms

The \(d^{3}\) terms are \(9d^{3}\) and \(-8d^{3}\). Combining them:
\(9d^{3}-8d^{3}=d^{3}\)

Step3: Combine like terms for \(d^{2}\) terms

The \(d^{2}\) terms are \(3d^{2}\) and \(-2d^{2}\). Combining them:
\(3d^{2}-2d^{2}=d^{2}\)

Step4: Combine like terms for \(d\) terms

The \(d\) terms are \(5d\) and \(-d\). Combining them:
\(5d - d = 4d\)

Step5: Combine like terms for constant terms

The constant terms are \(8\) and \(-1\). Combining them:
\(8 - 1=7\)

Step6: Combine all the results

Putting all the combined terms together, we get:
\(d^{3}+d^{2}+4d + 7\)

Answer:

\(d^{3}+d^{2}+4d + 7\)