Sure! Let's perform the subtraction step-by-step.
Step 1: Write down the given expressions.
We have two expressions:
1. \(9a^2 - 7b + 3c^3 - 4\)
2. \(6a^2 + 6b - 3c^3 - 4\)
Step 2: Set up the subtraction.
We need to subtract the second expression from the first:
[tex]\[
(9a^2 - 7b + 3c^3 - 4) - (6a^2 + 6b - 3c^3 - 4)
\][/tex]
Step 3: Distribute the negative sign across the second expression.
When we distribute the negative sign, we change the signs of each term in the second expression:
[tex]\[
(9a^2 - 7b + 3c^3 - 4) - 6a^2 - 6b + 3c^3 + 4
\][/tex]
Step 4: Combine like terms.
Next, we combine the terms with \(a^2\), \(b\), and \(c^3\):
- For \(a^2\) terms: \(9a^2 - 6a^2 = 3a^2\)
- For \(b\) terms: \(-7b - 6b = -13b\)
- For \(c^3\) terms: \(3c^3 + 3c^3 = 6c^3\)
- For constant terms: \(-4 + 4 = 0\)
So, the simplified result is:
[tex]\[
3a^2 - 13b + 6c^3
\][/tex]
Step 5: Check the given options.
We need to match our simplified result with the given options:
1. \(3a^2 - 13b + 6c^3\)
2. \(15a^2 - b - 8\)
3. \(-3a^2 + 13b - 6c^3\)
4. \(3a^2 - b\)
The correct option that matches our simplified result is:
[tex]\[
3a^2 - 13b + 6c^3
\][/tex]
Therefore, the correct choice is option 1.
