Add the expressions.
Expression 1: −3k+4k3−2
Expression 2: 9k2−3k3+4k−3
(2 points)
k3+
k2+
k+
To add the expressions −3k+4k^3−2 and 9k^2−3k^3+4k−3, we combine like terms.
First, let's combine all the terms with k^3: -3k^3 + 4k^3 = k^3.
Next, let's combine all the terms with k^2: 0k^2 + 9k^2 = 9k^2.
Now, let's combine all the terms with k: -3k + 4k = k.
Finally, let's combine the constants: -2 + (-3) = -5.
Putting it all together, we have the simplified expression:
k^3 + 9k^2 + k - 5.
To add the expressions −3k+4k^3−2 and 9k^2−3k^3+4k−3, we group the like terms together:
Combine the like terms with k^3:
(4k^3) + (-3k^3) = k^3
Combine the like terms with k^2:
(0k^2) + (9k^2) = 9k^2
Combine the like terms with k:
(-3k) + (4k) = k
Combine the constant terms:
(-2) + (-3) = -5
So, the simplified expression is:
k^3 + 9k^2 + k - 5
To add the expressions, we need to combine like terms. Like terms have the same variable raised to the same power. In this case, the variable is "k."
For the first expression: −3k + 4k^3 − 2
For the second expression: 9k^2 − 3k^3 + 4k − 3
We can start by combining the terms with "k^3." In the first expression, there is a term with "k^3," and in the second expression, there is also a term with "k^3." Therefore, we add those terms together:
(4k^3) + (-3k^3) = 4k^3 - 3k^3
The result is k^3.
Next, we combine the terms with "k^2." In the second expression, there is a term with "k^2" (9k^2), but there isn't any term with "k^2" in the first expression. So, the term with "k^2" in the second expression is simply carried over to the final expression:
k^3 + (9k^2)
Next, we combine the terms with "k." In the first expression, there is a term with "k" (-3k), and in the second expression, there is also a term with "k" (4k). Therefore, we add those terms together:
(-3k) + (4k) = -3k + 4k
The result is k.
Finally, there are no constant terms in either expression, so we don't have any numerical values like 2 or 3 to add.
Putting it all together, we have:
k^3 + 9k^2 + (k)
Therefore, the final expression after adding is k^3 + 9k^2 + k.