\[\boxed{\text{840.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ (a + b)^{2} + (a - b)^{2} = 2 \cdot (a^{2} + b^{2})\]
\[a² + 2ab + b² + a² - 2ab + b^{2} = 2a^{2} + 2b^{2}\]
\[2a^{2} + 2b^{2} = 2a^{2} + 2b^{2}\]
\[\textbf{б)}\ (a + b)^{2} - (a - b)^{2} = 4ab\]
\[a^{2} + 2ab + b^{2} - \left( a^{2} - 2ab + b^{2} \right) = 4ab\]
\[a² + 2ab + b² - a^{2} + 2ab - b^{2} = 4ab\]
\[4ab = 4ab\]
\[\textbf{в)}\ a^{2} + b^{2} = (a + b)^{2} - 2ab\]
\[a^{2} + b^{2} = a^{2} + 2ab + b^{2} - 2ab\]
\[a^{2} + b² = a^{2} + b²\]
\[\textbf{г)}\ (a + b)^{2} - 2b(a + b) = a^{2} - b²\]
\[a^{2} - b²a^{2} + 2ab + b^{2} - 2ab - 2b^{2} = a^{2} - b²\]
\[a^{2} - b^{2} = a^{2} - b²\]