Sure, let's go through the subtraction step by step:
We need to subtract the second expression from the first:
[tex]\[
\left(6a^2 - 7b + 3c^3 + 4\right) - \left(9a^2 + 6b - 3c^3 + 4\right)
\][/tex]
Step 1: Distribute the negative sign across the second expression.
[tex]\[
6a^2 - 7b + 3c^3 + 4 - 9a^2 - 6b + 3c^3 - 4
\][/tex]
Step 2: Combine like terms (terms with the same powers of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]):
[tex]\[
(6a^2 - 9a^2) + (-7b - 6b) + (3c^3 + 3c^3) + (4 - 4)
\][/tex]
Step 3: Perform the arithmetic for each set of like terms:
[tex]\[
(6a^2 - 9a^2) = -3a^2
\][/tex]
[tex]\[
(-7b - 6b) = -13b
\][/tex]
[tex]\[
(3c^3 + 3c^3) = 6c^3
\][/tex]
[tex]\[
(4 - 4) = 0
\][/tex]
Step 4: Combine the simplified terms:
[tex]\[
-3a^2 - 13b + 6c^3
\][/tex]
So, the result of the subtraction is:
[tex]\[
-3a^2 - 13b + 6c^3
\][/tex]
