Question

subtract.
\\((17r^2s + 10rs - 15 + 15r^2s^2) - (7sr^2 + 4 - 8r^2s^2)\\)
\\((17r^2s + 10rs - 15 + 15r^2s^2) - (7sr^2 + 4 - 8r^2s^2) = \square\\)
(simplify your answer. do not factor.)

Explanation:

Step1: Distribute the negative sign

First, we distribute the negative sign to each term inside the second parentheses:
$$(17r^{2}s + 10rs - 15 + 15r^{2}s^{2}) - 7sr^{2} - 4 + 8r^{2}s^{2}$$

Step2: Combine like terms for \(r^{2}s\) terms

The terms with \(r^{2}s\) are \(17r^{2}s\) and \(-7sr^{2}\) (note that \(sr^{2}=r^{2}s\)). Combining them:
\(17r^{2}s - 7r^{2}s = 10r^{2}s\)

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

The terms with \(r^{2}s^{2}\) are \(15r^{2}s^{2}\) and \(8r^{2}s^{2}\). Combining them:
\(15r^{2}s^{2}+ 8r^{2}s^{2}=23r^{2}s^{2}\)

Step4: Combine constant terms

The constant terms are \(-15\) and \(-4\). Combining them:
\(-15 - 4=-19\)

Step5: The \(10rs\) term remains as is since there are no other like terms.

Step6: Combine all the simplified terms

Putting it all together: \(10r^{2}s + 10rs - 19 + 23r^{2}s^{2}\) (we can also write the terms in standard form by degree, but the problem just asks to simplify, so this is acceptable)

Answer:

\(23r^{2}s^{2}+10r^{2}s + 10rs-19\)