Question

add the polynomials and find the sum of the expression.
Polynomials #1: -9m^3+15m^5-3m^2-14
Polynomials #2: 10-5m^2+8m-3m^5

what is the sum of the expression? simplify and combine like terms

Answer 1

To add the polynomials \(-9m^3 + 15m^5 - 3m^2 - 14\) and \(10 - 5m^2 + 8m - 3m^5\), we can combine like terms.

Let's first list both polynomials:

Polynomial #1:
\[
-9m^3 + 15m^5 - 3m^2 - 14
\]

Polynomial #2:
\[
10 - 5m^2 + 8m - 3m^5
\]

Now, we will add them together:

\[
(-9m^3 + 15m^5 - 3m^2 - 14) + (10 - 5m^2 + 8m - 3m^5)
\]

Next, we combine like terms:

1. **\(m^5\) terms**:
\[
15m^5 - 3m^5 = 12m^5
\]

2. **\(m^3\) term**:
\[
-9m^3 \quad (\text{there is no m}^3 \text{ term in the second polynomial})
\]

3. **\(m^2\) terms**:
\[
-3m^2 - 5m^2 = -8m^2
\]

4. **\(m\) term**:
\[
8m \quad (\text{there is no m term in the first polynomial})
\]

5. **Constant terms**:
\[
-14 + 10 = -4
\]

Putting it all together, we have:

\[
12m^5 - 9m^3 - 8m^2 + 8m - 4
\]

Thus, the sum of the expression is:

\[
\boxed{12m^5 - 9m^3 - 8m^2 + 8m - 4}
\]