\[\boxed{\text{843.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\textbf{а)}\ 2b² - 6b + 1 > 2b(b - 3)\]
\[2b^{2} - 6b + 1 > 2b^{2} - 6b\]
\[2b^{2} + 1 > 2b^{2}\]
\[1 > 0\]
\[\textbf{б)}\ (c + 2)(c + 6) <\]
\[< (c + 3)(c + 5)\]
\[c^{2} + 6c + 2c + 12 < c^{2} +\]
\[+ 5c + 3c + 15\]
\[c^{2} + 12 < c^{2} + 15\]
\[12 < 15\]
\[\textbf{в)}\ p(p + 7) > 7p - 1\]
\[p^{2} + 7p > 7p - 1\]
\[p^{2} > - 1,\ \ так\ как\ p^{2} > 0\]
\[\textbf{г)}\ 8y(3y - 10) < (5y - 8)²\]
\[24y^{2} - 80y < 25y^{2} - 80y + 64\]
\[24y^{2} < 25y^{2} + 64\]
\[y^{2} > - 64;\ \ так\ как\ y^{2} > 0\]