\[\boxed{\text{51\ (51)\ .\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ 5bc - 5c = 5c \cdot (b - 1)\]
\[\textbf{б)}\ 10n + 15n^{2} = 5n \cdot (2 + 3n)\]
\[\textbf{в)}\ 8ab + 12bc = 4b \cdot (2a + 3c)\]
\[\textbf{г)}\ 5y - 5x + y^{2} - xy =\]
\[= 5 \cdot (y - x) + y \cdot (y - x) =\]
\[= (y - x) \cdot (5 + y)\]
\[\textbf{д)}\ a^{2} - 9 = (a - 3) \cdot (a + 3)\]
\[\textbf{е)}\text{\ x}^{2} + 10x + 25 = ({x + 5)}^{2} =\]
\[= (x + 5)(x + 5)\]
\[\textbf{ж)}\ y^{2} - 2y + 1 = ({y - 1)}^{2} =\]
\[= (y - 1)(y - 1)\]
\[\textbf{з)}\text{\ a}^{3} + 64 =\]
\[= (a + 4) \cdot (a^{2} - 4a + 16)\]
\[\textbf{и)}\ b^{3} - 1 =\]
\[= (b - 1) \cdot (b^{2} + b + 1)\]