https://file.aiquickdraw.com/mathbot/file/1725839800992pepvfe4h.jpg

The expression provided in the image is:

\[
x^2 + 4y^2 + 25z^2 - 4xy - 20yz - 10xz
\]

We are given the values \(x = 4\), \(y = 2\), and \(z = 3\). Let’s substitute these values into the expression and simplify.

\[
(4)^2 + 4(2)^2 + 25(3)^2 - 4(4)(2) - 20(2)(3) - 10(4)(3)
\]

Now, I will calculate the result step by step.

\[
16 + 4(4) + 25(9) - 4(8) - 20(6) - 10(12)
\]

Let me calculate this.The value of the expression when \(x = 4\), \(y = 2\), and \(z = 3\) is \(-15\).

Would you like further clarification or details on any step?

Here are 5 related questions you could explore:
1. What happens if we change the value of \(z\) in the given expression?
2. How does the expression simplify if the \(xy\), \(yz\), and \(xz\) terms are removed?
3. What would the value of the expression be if \(x = y = z = 1\)?
4. Can we generalize this expression for other values of \(x\), \(y\), and \(z\)?
5. What role do the coefficients of the variables play in determining the result?

**Tip:** Always substitute values carefully and follow the order of operations (PEMDAS) to avoid errors in multi-variable expressions.

Find the value of x^2 + 4y^2 + 25z^2 - 4xy - 20yz - 10xz while x = 4, y = 2 and z = 3.

This math problem involves evaluating a multivariable expression by substituting specific values for x, y, and z. The solution includes step-by-step simplification, perfect for students in Grades 9-10 studying algebra.

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