Add the expressions:

Question

Expression 1: -3k + 4k^3 - 2
Expression 2: 9k^2 - 3k^3 + 4k - 3

___k^3 + ___k^2 + ___k + ___

the ___ shows the blank and what you need to answer

Answer 1

To add the two expressions, we first align like terms:

1. Expression 1: -3k + 4k^3 - 2
2. Expression 2: 9k^2 - 3k^3 + 4k - 3

Now, let's combine the terms:

• For \(k^3\): \[ 4k^3 - 3k^3 = 1k^3 \]

• For \(k^2\): \[ 0 + 9k^2 = 9k^2 \]

• For \(k\): \[ -3k + 4k = 1k \]

• For the constant: \[ -2 - 3 = -5 \]

Now, we can write the combined expression as: \[ 1k^3 + 9k^2 + 1k - 5 \]

In terms of the blanks:

• The coefficient of \(k^3\) is 1.
• The coefficient of \(k^2\) is 9.
• The coefficient of \(k\) is 1.
• The constant is -5.

So the final answer is: \[ 1k^3 + 9k^2 + 1k - 5 \]

Which fills the blanks: ___k^3 + ___k^2 + ___k + ___ becomes 1 for \(k^3\), 9 for \(k^2\), 1 for \(k\), and -5 for the constant.