1. **State the problem:** Expand the expression $$(4x^2 + y^4)^2$$ and write the answer as a polynomial in standard form. 2. **Recall the formula:** The square of a binomial $$(a + b)^2$$ is given by $$a^2 + 2ab + b^2$$. 3. **Identify terms:** Here, $$a = 4x^2$$ and $$b = y^4$$. 4. **Apply the formula:** $$ (4x^2 + y^4)^2 = (4x^2)^2 + 2 \times (4x^2) \times y^4 + (y^4)^2 $$ 5. **Calculate each term:** - $$(4x^2)^2 = 16x^4$$ - $$2 \times (4x^2) \times y^4 = 8x^2y^4$$ - $$(y^4)^2 = y^8$$ 6. **Write the expanded polynomial:** $$ 16x^4 + 8x^2y^4 + y^8 $$ 7. **Final answer:** The polynomial in standard form is $$16x^4 + 8x^2y^4 + y^8$$.