Question: simplify $72y^4-50x^4$
1. **State the problem:** Simplify the expression $$72y^4 - 50x^4$$.
2. **Identify common factors:** Both terms have a common factor of 2.
3. **Factor out the common factor:**
$$72y^4 - 50x^4 = 2(36y^4 - 25x^4)$$
4. **Recognize difference of squares:**
$$36y^4 - 25x^4 = (6y^2)^2 - (5x^2)^2$$
5. **Apply difference of squares formula:**
$$a^2 - b^2 = (a - b)(a + b)$$
6. **Factor the expression:**
$$2(6y^2 - 5x^2)(6y^2 + 5x^2)$$
7. **Final simplified form:**
$$\boxed{2(6y^2 - 5x^2)(6y^2 + 5x^2)}$$
This is the fully factored and simplified form of the original expression.