\[\boxed{\text{Контрольные}\text{\ }\text{вопросы}\text{\ }\text{и}\text{\ }\text{задания}\text{\ }\text{к}\text{\ }\text{параграфу}\text{\ }\text{12.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\boxed{\text{1.}\text{\ }}\]
\[Формула\ квадрата\ суммы:\]
\[(a + b)^{2} = a^{2} + 2ab + b^{2}.\]
\[Доказательство:\]
\[(a + b)^{2} = (a + b)(a + b) =\]
\[= a^{2} + 2ab + b^{2}.\]
\[\boxed{\text{2.}\text{\ }}\]
\[Формула\ квадрата\ разности:\]
\[(a - b)^{2} = a^{2} - 2ab + b^{2}.\]
\[Доказательство:\]
\[(a - b)^{2} = (a - b)(a - b) =\]
\[= a^{2} - 2ab + b^{2}.\]
\[\boxed{\text{3.}\text{\ }}\]
\[25y^{2} + 40y + 16 = (5y + 4)^{2}\]
\[\boxed{\text{4.}\text{\ }}\]
\[81x^{2} - 18x + 1 = (9x - 1)^{2}\]
\[\boxed{\text{5.}\text{\ }}\]
\[Формула\ куба\ суммы:\]
\[(a + b)^{3} =\]
\[= a^{3} + 3a^{2}b + 3ab^{2} + b^{3}.\]
\[Пример:\ \]
\[(a + 2b)^{3} =\]
\[= a^{3} + 6a^{2}b + 12ab^{2} + 8b^{3}.\]
\[\boxed{\text{6.}\text{\ }}\]
\[Формула\ куба\ разности:\]
\[(a - b)^{3} =\]
\[= a^{3} - 3a^{2}b + 3ab^{2} - b^{3}.\]
\[(3x - y)^{3} =\]
\[= 27x^{3} - 27x^{2}y + 9xy^{2} - y^{3}.\]