Add the expressions.
Expression 1: −3k+4k3−2
Expression 2: 9k2−3k3+4k−3
Expression 1 + Expression 2:
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3) = (-3k + 4k^3 - 2 + 9k^2 - 3k^3 + 4k - 3)
Combine like terms:
-3k + 4k^3 + 9k^2 - 3k^3 + 4k - 2 - 3
= 4k^3 - 3k^3 + 9k^2 - 3k + 4k - 3k - 2 - 3
= (4k^3 - 3k^3) + 9k^2 + (4k - 3k) + (-2 - 3)
Simplify:
k^3 + 9k^2 + k - 5
To add the expressions −3k+4k^3−2 and 9k^2−3k^3+4k−3, we will combine like terms.
First, let's group the terms that have the same variable and exponent:
- For the k terms, we have: -3k + 4k^3 - 3k^3 + 4k
- For the constant terms, we have: -2 - 3
Now, let's simplify each group:
- For the k terms: -3k + 4k^3 - 3k^3 + 4k = (4k^3 - 3k^3) + (-3k + 4k) = k^3 + k.
- For the constant terms: -2 - 3 = -5.
Finally, let's put the simplified groups together:
The sum of the expressions −3k+4k^3−2 and 9k^2−3k^3+4k−3 is given by:
k^3 + k - 5.