The difference of the product of x and y and z

The expression "the difference of the product of \( x \) and \( y \) and \( z \)" can be translated into a mathematical expression as follows:

The product of \( x \) and \( y \) is \( xy \).

The difference between this product and \( z \) is \( xy - z \).

So, the final expression is:

\[
xy - z
\]

Would you like further details or have any questions?

Here are 5 related questions to explore further:

1. What is the sum of the product of \( x \) and \( y \) and \( z \)?
2. How does the expression change if \( z \) is subtracted first, and then multiplied by \( x \) and \( y \)?
3. If \( x = 2 \), \( y = 3 \), and \( z = 4 \), what is the value of \( xy - z \)?
4. What happens if \( x \), \( y \), and \( z \) are all negative numbers?
5. How would this expression look if \( x \), \( y \), and \( z \) were vectors instead of scalars?

**Tip:** When translating word problems into mathematical expressions, look out for key terms like "product," "sum," and "difference" to set up the correct operations.

Explore how to calculate the difference of the product of x, y, and z in mathematics. Learn the step-by-step process to express this problem mathematically and solve it effectively. Suitable for students in Grades 7-9.

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