Subtract 3xy + 5yz-7zx from 5xy-2yz-2zx + 10xyz

To subtract the expression \( (3xy + 5yz - 7zx) \) from \( (5xy - 2yz - 2zx + 10xyz) \), follow these steps:

### Step 1: Write down the subtraction as an equation:
\[
(5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx)
\]

### Step 2: Distribute the negative sign across the second expression:
\[
5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx
\]

### Step 3: Combine like terms:
- For \( xy \): \( 5xy - 3xy = 2xy \)
- For \( yz \): \( -2yz - 5yz = -7yz \)
- For \( zx \): \( -2zx + 7zx = 5zx \)
- For \( xyz \): there’s no corresponding term in the second expression, so it remains \( 10xyz \)

### Final result:
\[
2xy - 7yz + 5zx + 10xyz
\]

Let me know if you need further clarification or details.

Here are 5 related questions to expand this topic:
1. What happens if we add \( 3xy + 5yz - 7zx \) instead of subtracting?
2. How do we factor common terms from expressions like these?
3. How do these kinds of expressions behave when multiplied together?
4. Can these expressions be represented geometrically in terms of area or volume?
5. How do we solve similar expressions involving more variables?

**Tip**: Always distribute negative signs carefully when subtracting entire expressions to avoid sign errors!

Subtract 3xy + 5yz - 7zx from 5xy - 2yz - 2zx + 10xyz

Learn how to subtract the polynomial expression 3xy + 5yz - 7zx from 5xy - 2yz - 2zx + 10xyz, with a detailed step-by-step solution. This problem covers key algebraic concepts such as polynomial subtraction and combining like terms. Suitable for students in Grades 9-10.

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