We can simplify the expression \(\frac{-14x^3y^4 + 21x^2y^4}{7xy}\) step by step.

### Step 1: Factor out the common term in the numerator
First, we notice that both terms in the numerator have a common factor of \(7x^2y^4\). Let's factor it out:

\[
\frac{-14x^3y^4 + 21x^2y^4}{7xy} = \frac{7x^2y^4(-2x + 3)}{7xy}
\]

### Step 2: Cancel out common terms
Now, cancel out the common factor of \(7xy\) from both the numerator and denominator:

\[
= \frac{x^2y^4(-2x + 3)}{xy}
\]

When dividing powers of variables:
- \(x^2 / x = x\)
- \(y^4 / y = y^3\)

Thus, the expression becomes:

\[
= x y^3(-2x + 3)
\]

### Final Answer:
\[
xy^3(-2x + 3)
\]

Let me know if you want further details, or if you have any questions!

Here are 5 related questions to expand your understanding:
1. How do you factor out terms from polynomials?
2. What is the rule for canceling out common variables in fractions?
3. Can you simplify \(\frac{6x^4y^3 - 18x^3y^2}{3x^2y}\)?
4. What happens when you have negative exponents in the numerator and denominator?
5. How does factoring help in simplifying algebraic expressions?

**Tip:** Always look for common factors in the numerator and denominator before canceling to simplify expressions faster.

Learn how to simplify the algebraic expression (-14x^3y^4 + 21x^2y^4) / 7xy by factoring and canceling common terms. This solution involves key algebraic concepts like factoring, the distributive property, and the laws of exponents. Suitable for students in Grades 8-10.

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