The image you've uploaded contains a math problem involving algebraic expressions and the evaluation of a specific expression. Let's break it down step by step.

From the image, the goal is to evaluate the following expression:

$3(a^2 - 2ab - b^2) - (4a^2 + ab + b^2)$ with $a = 3$ and $b = 1$.

Substituting the values of $a = 3$ and $b = 1$:

$3((3)^2 - 2(3)(1) - (1)^2) - (4(3)^2 + (3)(1) + (1)^2)$

First, calculate the squares and products:

$3(9 - 6 - 1) - (4(9) + 3 + 1)$

Simplify the expressions inside the parentheses:

$3(9 - 6 - 1) = 3(2) = 6$ and $4(9) + 3 + 1 = 36 + 3 + 1 = 40$

Now, substitute these simplified results back into the expression:

$6 - 40 = -34$

Thus, the value of the expression is $-34$.

Let me know if you need further explanation or have any questions about this solution!

Here are some related questions that you may find interesting:

1. How would the value of the expression change if $a = 2$ and $b = 4$?
2. How can you simplify similar expressions with multiple variables?
3. What is the significance of factoring in simplifying expressions like this one?
4. How do algebraic identities help in solving problems like this one?
5. Can this type of expression appear in a real-world application, such as in physics or economics?

Tip: Always check if factoring or combining like terms can simplify your calculations before substituting values!