Let's solve the expression step by step:

The given expression is: $7(7 - 3) + (-7)^2 - 6$

Step 1: Simplify inside the parentheses.

$7 - 3 = 4$ Now, substitute this back into the expression: $7(4) + (-7)^2 - 6$

Step 2: Multiply.

$7 \times 4 = 28$ Now the expression becomes: $28 + (-7)^2 - 6$

Step 3: Calculate the exponent.

$(-7)^2 = 49$ So now the expression is: $28 + 49 - 6$

Step 4: Perform the addition and subtraction.

$28 + 49 = 77$ $77 - 6 = 71$

Thus, the value of the expression is: $\boxed{71}$

Would you like more details or have any questions?

Here are five related questions to explore:

1. What would the result be if the exponent were $(-7)^3$ instead of $(-7)^2$?
2. How does the sign of the base in the exponent affect the outcome?
3. Can you solve a similar expression like $5(6 - 2) + (-5)^2 - 4$?
4. How would the result change if we added a division step, such as $7(7 - 3) + (-7)^2 - 6 \div 2$?
5. What would the result be if the constant term were positive instead of $-6$?

Tip: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to solve expressions accurately.