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.