1. **State the problem:** Simplify the expression $(-2x+3y)^2-(y+x)^2$. 2. **Recall the formula:** Use the difference of squares formula: $$a^2 - b^2 = (a-b)(a+b)$$ where $a = -2x+3y$ and $b = y+x$. 3. **Apply the formula:** $$(-2x+3y)^2-(y+x)^2 = \big((-2x+3y)-(y+x)\big) \cdot \big((-2x+3y)+(y+x)\big)$$ 4. **Simplify each factor:** - First factor: $$(-2x+3y)-(y+x) = -2x+3y - y - x = (-2x - x) + (3y - y) = -3x + 2y$$ - Second factor: $$(-2x+3y)+(y+x) = -2x + 3y + y + x = (-2x + x) + (3y + y) = -x + 4y$$ 5. **Write the product:** $$(-3x + 2y)(-x + 4y)$$ 6. **Expand the product:** $$(-3x)(-x) + (-3x)(4y) + (2y)(-x) + (2y)(4y) = 3x^2 - 12xy - 2xy + 8y^2$$ 7. **Combine like terms:** $$3x^2 - 14xy + 8y^2$$ **Final answer:** $$3x^2 - 14xy + 8y^2$$