Question

Afd the expressions.

Expression 1: −3k+4k3−2
−
3
𝑘
+
4
𝑘
3
−
2


Expression 2: 9k2−3k3+4k−3

Answer 1

To combine the two expressions, \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we need to group the like terms together.

### Step 1: Write each expression.
- Expression 1: \( -3k + 4k^3 - 2 \)
- Expression 2: \( 9k^2 - 3k^3 + 4k - 3 \)

### Step 2: Combine the two expressions.
Now, let's write them together:
\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

### Step 3: Combine like terms.
- \( k^3 \) terms: \( 4k^3 - 3k^3 = 1k^3 \)
- \( k^2 \) terms: \( 9k^2 \) (there are no other \( k^2 \) terms to combine with)
- \( k \) terms: \( -3k + 4k = 1k \)
- Constant terms: \( -2 - 3 = -5 \)

### Step 4: Write the final simplified expression.
Combining all the results gives us:
\[
k^3 + 9k^2 + k - 5
\]

Thus, the resulting expression after combining the two is:
\[
k^3 + 9k^2 + k - 5
\]