Problem

Subtract the polynomials.
\[
\left(5 a^{5}+7 a^{2}-4\right)-\left(9 a^{5}-5 a^{2}+18\right)
\]

Answer

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Answer

\(\boxed{-4 a^{5} + 12 a^{2} - 22}\) is the result of the subtraction.

Steps

Step 1 :Given two polynomials \(5 a^{5}+7 a^{2}-4\) and \(9 a^{5}-5 a^{2}+18\), we are asked to subtract the second polynomial from the first.

Step 2 :To subtract polynomials, we subtract the corresponding terms in the two polynomials. In this case, we subtract the coefficients of the \(a^{5}\) terms, the \(a^{2}\) terms, and the constant terms separately.

Step 3 :Subtracting the \(a^{5}\) terms: \(5 a^{5} - 9 a^{5} = -4 a^{5}\)

Step 4 :Subtracting the \(a^{2}\) terms: \(7 a^{2} - (-5 a^{2}) = 12 a^{2}\)

Step 5 :Subtracting the constant terms: \(-4 - 18 = -22\)

Step 6 :Combining these results, we get the final polynomial: \(-4 a^{5} + 12 a^{2} - 22\)

Step 7 :\(\boxed{-4 a^{5} + 12 a^{2} - 22}\) is the result of the subtraction.

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