Add the expressions.

Question

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


Expression 2: 9k2−3k3+4k−3
9
𝑘
2
−
3
𝑘
3
+
4
𝑘
−
3


(2 points)
k3+
𝑘
3
+
k2+
𝑘
2
+
k+
𝑘
+

Answer 1

To add the two expressions, we'll combine like terms from both the expressions:

Expression 1: \[ -3k + 4k^3 - 2 \]

Expression 2: \[ 9k^2 - 3k^3 + 4k - 3 \]

Now, let's reorganize each expression by grouping like terms:

From Expression 1:

• \(4k^3\) (cubic term),
• \(-3k\) (linear term),
• \(-2\) (constant).

From Expression 2:

• \(-3k^3\) (cubic term),
• \(9k^2\) (quadratic term),
• \(4k\) (linear term),
• \(-3\) (constant).

Now let's combine the like terms:

1. Combine the \(k^3\) terms: \[ 4k^3 - 3k^3 = 1k^3 = k^3 \]

2. Combine the \(k^2\) terms: \[ 0 + 9k^2 = 9k^2 \]

3. Combine the \(k\) terms: \[ -3k + 4k = 1k = k \]

4. Combine the constant terms: \[ -2 - 3 = -5 \]

Putting it all together, we get: \[ k^3 + 9k^2 + k - 5 \]

So the final result after adding the two expressions is: \[ k^3 + 9k^2 + k - 5 \]