To solve the expression \( 4x^4 + 3|4x - 9| \) when \( x = -2 \), let's break it down step by step.

### Step 1: Substitute \( x = -2 \) into the expression

\[
4x^4 + 3|4x - 9|
\]
Substitute \( x = -2 \):

\[
4(-2)^4 + 3|4(-2) - 9|
\]

### Step 2: Calculate \( 4(-2)^4 \)
\[
(-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16
\]
So:
\[
4 \times 16 = 64
\]

### Step 3: Simplify the absolute value \( |4(-2) - 9| \)

\[
4(-2) = -8
\]
So:
\[
-8 - 9 = -17
\]
Now take the absolute value:
\[
| -17 | = 17
\]

### Step 4: Multiply and add the terms

\[
3 \times 17 = 51
\]
Now add the two results:
\[
64 + 51 = 115
\]

### Final Answer:
\[
115
\]

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:
1. How do you handle expressions with higher powers like \( x^4 \)?
2. What are the properties of absolute value in algebraic expressions?
3. Can you solve a similar problem for a different value of \( x \)?
4. How do polynomial expressions change when you substitute negative values for \( x \)?
5. What are the differences between evaluating polynomials and evaluating absolute value functions?

**Tip**: Always remember to apply the absolute value operation after simplifying everything inside the bars!

Learn how to solve the algebraic expression 4x^4 + 3|4x - 9| by substituting x = -2. This step-by-step solution breaks down polynomial evaluation, the absolute value function, and exponent rules. Suitable for students in Grades 9-12.

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