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.

Learn how to solve the algebraic expression 7(7-3) + (-7)^2 - 6 by following the order of operations (PEMDAS). This step-by-step guide simplifies the problem by calculating inside parentheses, handling exponents, and performing multiplication, addition, and subtraction. Suitable for students in Grades 6-8.

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