https://file.aiquickdraw.com/mathbot/file/172513384344209ht9sfo.jpg

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.

Learn how to add two polynomials and express the result in standard form. This problem covers combining like terms and writing polynomials in standard form, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation