https://file.aiquickdraw.com/mathbot/file/1729705380028yin64lqj.jpg

Let's evaluate the given expression step-by-step.

We are given the expression:

\[
x^2y - x(yz^3)
\]

with the values \( x = -2 \), \( y = 7 \), and \( z = -4 \).

### Step 1: Compute \( x^2y \)

\[
x^2 = (-2)^2 = 4
\]

Now, multiply this by \( y = 7 \):

\[
x^2y = 4 \times 7 = 28
\]

### Step 2: Compute \( x(yz^3) \)

First, compute \( z^3 \):

\[
z^3 = (-4)^3 = -64
\]

Now multiply this by \( y = 7 \):

\[
yz^3 = 7 \times (-64) = -448
\]

Next, multiply this by \( x = -2 \):

\[
x(yz^3) = -2 \times (-448) = 896
\]

### Step 3: Subtract the results

\[
x^2y - x(yz^3) = 28 - 896 = -868
\]

### Final Answer:
The value of the expression is:

\[
\boxed{-868}
\]

Would you like more details or have any questions?

Here are five related questions to expand your understanding:
1. What happens if we change \( x \), \( y \), or \( z \) to different values?
2. How do powers of negative numbers affect the result?
3. What is the impact of distributing \( x \) across \( yz^3 \) in this problem?
4. How would this expression change if you switch the order of multiplication in the second term?
5. What are the steps to simplifying more complex algebraic expressions involving exponents?

**Tip**: Always be careful with negative signs, especially when raising numbers to odd powers like cubes!

If x = -2, y = 7, and z = -4, evaluate the expression x^2y - x(yz^3).

Learn how to evaluate the algebraic expression x^2y - x(yz^3) step by step using given values for x, y, and z. This problem demonstrates the use of exponentiation and algebraic distribution. Suitable for Grades 8-10, it covers key concepts like powers of numbers and handling negative values.

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