1. **State the problem:** We are given the polynomial $$xy^2 - 2x^2y + 3y^3 - 6x^2y + 4xy^2$$ and told that Alina wrote the last term as $$3y^3$$. We need to find the first term of the polynomial in standard form. 2. **Combine like terms:** Group terms with the same variables and powers. - Terms with $$xy^2$$: $$xy^2 + 4xy^2 = 5xy^2$$ - Terms with $$x^2y$$: $$-2x^2y - 6x^2y = -8x^2y$$ - Term with $$y^3$$: $$3y^3$$ 3. **Write the polynomial with combined terms:** $$5xy^2 - 8x^2y + 3y^3$$ 4. **Standard form:** Polynomials are usually written in descending order of degree. The degrees of the terms are: - $$5xy^2$$ has degree $$1 + 2 = 3$$ - $$-8x^2y$$ has degree $$2 + 1 = 3$$ - $$3y^3$$ has degree $$3$$ Since all terms have degree 3, order by convention or lex order. Usually, terms with higher powers of $$x$$ come first. So the first term is $$-8x^2y$$. **Final answer:** $$-8x^2y$$