To solve the equation \( g(v-8) = (v-8)^2 - 7(v-8) \), we'll first simplify the right-hand side.

### Step 1: Expand and simplify the right-hand side
The equation is given as:

\[
g(v-8) = (v-8)^2 - 7(v-8)
\]

1. **Expand \( (v-8)^2 \):**
   \[
   (v-8)^2 = v^2 - 16v + 64
   \]

2. **Distribute the \(-7\) across \( (v-8) \):**
   \[
   -7(v-8) = -7v + 56
   \]

3. **Combine these results:**
   \[
   g(v-8) = v^2 - 16v + 64 - 7v + 56
   \]

4. **Combine like terms:**
   \[
   g(v-8) = v^2 - 23v + 120
   \]

### Final Answer:
\[
g(v-8) = v^2 - 23v + 120
\]

Would you like further details on this process, or do you have any questions?

### Related Questions:
1. How would you solve \( g(v) \) if \( g(v) = v^2 - 23v + 120 \)?
2. What would the graph of \( g(v-8) = v^2 - 23v + 120 \) look like?
3. Can you find the roots of the equation \( g(v-8) = 0 \)?
4. How would the function change if the constant term were different, say \( g(v-8) = v^2 - 23v + 130 \)?
5. What does the function \( g(v) = v^2 - 23v + 120 \) tell us about its behavior (vertex, direction, etc.)?

### Tip:
When working with quadratic expressions, always remember to expand, simplify, and combine like terms systematically to avoid mistakes.

Explore the process of simplifying the quadratic expression g(v-8) = (v-8)^2 - 7(v-8). This detailed step-by-step solution highlights key algebraic concepts like expansion, distributive property, and combining like terms. Ideal for students in Grades 8-10.

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