\[\boxed{\text{699}\text{\ (699)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[S_{n} = n^{2} - 8n,\ \ \]
\[x_{1} = S_{1} = 1^{2} - 8 \cdot 1 = - 7,\]
\[x_{2} = S_{2} - S_{1} = 2^{2} - 8 \cdot 2 + 7 = - 5,\]
\[x_{3} = S_{3} - S_{2} = (9 - 24) + 12 = - 3,\ \]
\[d = x_{2} - x_{1} = - 5 + 7 = 2,\]
\[S_{n} = \frac{2x_{1} + d(n - 1)}{2} \cdot n = \frac{- 14 + 2 \cdot (n - 1)}{2} \cdot n = n(n - 8) = n^{2} - 8n,\]
\[\Longrightarrow данная\ последовательность\ является\ арифметической\ \]
\[прогрессией.\]
\[\Longrightarrow x_{5} = x_{1} + 4d = - 7 + 4 \cdot 2 = 1.\]
\[\boxed{\text{699.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ (x - 2y)(x + 2y) + 4y² =\]
\[= x^{2} + 2yx - 2yx - 4y^{2} + 4y^{2} =\]
\[= x²\]
\[\textbf{б)}\ (2a - 3b)(2a + 3b) - 3a^{2} =\]
\[= 4a^{2} - 9b^{2} - 3a^{2} = a^{2} - 9b²\]
\[\textbf{в)}\ (5x - 1)^{2} + 10x =\]
\[= 25x^{2} - 10x + 1 + 10x =\]
\[= 25x^{2} + 1\]
\[\textbf{г)}\ (3y + 4z)² - 8z(3y - 2z) =\]
\[= 9y^{2} + 32z²\]
\[c^{6} + 64d^{3} - c^{6} + c^{2} =\]
\[= 64d^{3} + c^{2}\]