Question

simplify.
\\((5y^3 - 6y^2 + 2y + 1) - (-2y^3 + 7y + 10)\\)
\\((5y^3 - 6y^2 + 2y + 1) - (-2y^3 + 7y + 10) = 7y^3 - 6y^2 - 5y - 9\\) (do not factor)

Explanation:

Step1: Distribute the negative sign

To simplify the expression \((5y^{3}-6y^{2}+2y + 1)-(-2y^{3}+7y + 10)\), we first distribute the negative sign to each term inside the second parentheses. This gives us:
\(5y^{3}-6y^{2}+2y + 1 + 2y^{3}-7y - 10\)

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

The terms with \(y^{3}\) are \(5y^{3}\) and \(2y^{3}\). Combining these, we have:
\(5y^{3}+2y^{3}=7y^{3}\)

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

The term with \(y^{2}\) is \(-6y^{2}\), and there are no other \(y^{2}\) terms to combine with it, so it remains \(-6y^{2}\).

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

The terms with \(y\) are \(2y\) and \(-7y\). Combining these, we get:
\(2y-7y=-5y\)

Step5: Combine constant terms

The constant terms are \(1\) and \(-10\). Combining these, we have:
\(1 - 10=-9\)

Step6: Combine all combined terms

Putting all the combined terms together, we get:
\(7y^{3}-6y^{2}-5y - 9\)

Answer:

\(7y^{3}-6y^{2}-5y - 9\)