Question

Subtract the polynomials. Indicate the degree of the resulting polynomial.
(x^3+6xy+3y^2) - (4x^3+9xy+y^2)

(x^3+6xy+3y^2) - (4x^3+9xy+y^2) = blank

Answer 1

To subtract the polynomials \((x^3 + 6xy + 3y^2) - (4x^3 + 9xy + y^2)\), we distribute the negative sign to the second polynomial and then combine like terms.

Here's the subtraction step by step:

1. Rewrite the expression:
\[
x^3 + 6xy + 3y^2 - (4x^3 + 9xy + y^2)
\]

2. Distribute the negative sign:
\[
x^3 + 6xy + 3y^2 - 4x^3 - 9xy - y^2
\]

3. Combine like terms:
- For \(x^3\): \(x^3 - 4x^3 = -3x^3\)
- For \(xy\): \(6xy - 9xy = -3xy\)
- For \(y^2\): \(3y^2 - y^2 = 2y^2\)

Putting it all together, we have:
\[
-3x^3 - 3xy + 2y^2
\]

Now, let's determine the degree of the resulting polynomial. The degree is the highest power of \(x\) or \(y\) in the polynomial.

- The term \(-3x^3\) has a degree of 3.
- The term \(-3xy\) has a degree of \(1 + 1 = 2\).
- The term \(2y^2\) has a degree of 2.

The highest degree is 3, so the degree of the resulting polynomial is 3.

**Final Answer:**
\[
-3x^3 - 3xy + 2y^2
\]
Degree: 3