simplify the given expression

4x-4y
______
y-x

To simplify the expression:

\[
\frac{4x - 4y}{y - x}
\]

First, factor the numerator and denominator if possible.

1. Factor the numerator \( 4x - 4y \):
\[
4x - 4y = 4(x - y)
\]

2. Rewrite the denominator \( y - x \) as \( -(x - y) \):
\[
y - x = -(x - y)
\]

Now substitute these factored forms back into the expression:
\[
\frac{4(x - y)}{-(x - y)}
\]

The \( (x - y) \) terms cancel out, leaving:
\[
\frac{4}{-1} = -4
\]

Thus, the simplified expression is:
\[
\boxed{-4}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you factor common terms in an algebraic expression?
2. What happens when you divide two terms that are opposites?
3. Can you simplify \(\frac{x^2 - y^2}{y - x}\)?
4. How do you handle negative signs in fractions?
5. What are other methods of simplifying expressions involving variables?

**Tip:** Always look for common factors or patterns when simplifying algebraic expressions.

simplify the given expression 4x - 4y / (y - x)

Learn how to simplify the algebraic expression 4x - 4y / (y - x) by factoring and cancelling terms. This step-by-step solution covers algebraic concepts such as factoring and dealing with negative signs in denominators. Suitable for students in Grades 8-10.

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