To find the expression that equals \(2C - 3B\) and put it in standard form, we first need to express \(C\) and \(B\) based on the provided definitions.
Step 1: Write down the expressions for \(C\) and \(B\).
- For \(C\): \[ C = 1 + 5n - 6n^2 \]
- For \(B\): \[ B = n + 4n^2 \]
Step 2: Calculate \(3B\).
Now, let's compute \(3B\): \[ 3B = 3(n + 4n^2) = 3n + 12n^2 \]
Step 3: Calculate \(2C\).
Next, we compute \(2C\): \[ 2C = 2(1 + 5n - 6n^2) = 2 + 10n - 12n^2 \]
Step 4: Compute \(2C - 3B\).
Now we subtract \(3B\) from \(2C\): \[ 2C - 3B = (2 + 10n - 12n^2) - (3n + 12n^2) \]
Step 5: Simplify the expression.
Combine like terms: \[ = 2 + (10n - 3n) + (-12n^2 - 12n^2) \] \[ = 2 + 7n - 24n^2 \]
Step 6: Write the expression in standard form.
The final expression in standard form, where we typically write terms in descending powers of \(n\), is: \[ -24n^2 + 7n + 2 \]
Thus, the expression that equals \(2C - 3B\) in standard form is: \[ \boxed{-24n^2 + 7n + 2} \]