Let's solve the given problem by adding the two polynomials and expressing the result in standard form.

The expression to add is:

$(-4y^3 - 5y + 16) + (4y^2 - y + 9)$

Step 1: Combine Like Terms

• The $y^3$ term: There is only one $y^3$ term, $-4y^3$.
• The $y^2$ term: There is only one $y^2$ term, $4y^2$.
• The $y$ term: Combine $-5y$ and $-y$.
• The constant term: Combine $16$ and $9$.

Step 2: Perform the Addition

• $y^3$ term: $-4y^3$
• $y^2$ term: $4y^2$
• $y$ term: $-5y - y = -6y$
• Constant term: $16 + 9 = 25$

Step 3: Write the Final Expression in Standard Form

The standard form is:

$-4y^3 + 4y^2 - 6y + 25$

So, the expanded polynomial in standard form is:

$\boxed{-4y^3 + 4y^2 - 6y + 25}$

Would you like more details on any of these steps or have any questions?

Related Questions:

1. How do you add polynomials with more than three terms?
2. What is the standard form of a polynomial?
3. How would you subtract instead of add these two polynomials?
4. How do you factor the polynomial $-4y^3 + 4y^2 - 6y + 25$?
5. What are the general steps to simplify a polynomial?

Tip:

When adding polynomials, always ensure you align like terms (same degree) before combining them. This helps in avoiding errors and keeping the polynomial in standard form.