$(2ab - 1/2a^3)^2 = (2ab)^2 + (2 * 2ab * -1/2a^3) + (-1/2a^3)^2 = 4a^2b^2 + (-2a^4b) + 1/4a^6$

15. $(\sqrt{5} - 2\sqrt{2})^2 = (\sqrt{5})^2 + (2 * \sqrt{5} * -2\sqrt{2}) + (-2\sqrt{2})^2 = 5 - 4\sqrt{10} + 8$

$(4 - 3\sqrt{3})^2 = 4^2 + (2 * 4 * -3\sqrt{3}) + (-3\sqrt{3})^2 = 16 - 24\sqrt{3} + 27$

$(2x + 3y^2)^2 = (2x)^2 + (2 * 2x * 3y^2) + (3y^2)^2 = 4x^2 + 12xy^2 + 9y^4$

20. $(ab - 1/3)^2 = (ab)^2 + (2 * ab * -1/3) + (-1/3)^2 = a^2b^2 - 2/3ab + 1/9$

$(a^2 - 1/a^2)^2 = (a^2)^2 + (2 * a^2 * -1/a^2) + (-1/a^2)^2 = a^4 - 2 + 1/a^4$

$(4a - b)^2 = (4a)^2 + (2 * 4a * -b) + (-b)^2 = 16a^2 - 8ab + b^2$