ГДЗ по алгебре и начала математического анализа 10 класс Колягин Задание 10

\[\boxed{\mathbf{10}.}\]

\[1)\ 3a^{2} + 12ab + 12b^{2} =\]

\[= 3 \cdot \left( a^{2} + 4ab + 4b^{2} \right) =\]

\[= 3 \cdot (a + 2b)(a + 2b)\]

\[2)\ 6a^{3}b^{2} - 36a^{2}b^{3} + 54ab^{4} =\]

\[= 6ab^{2}\left( a^{2} - 6ab + 9b^{2} \right) =\]

\[= 6ab^{2}(a - 3b)(a - 3b)\]

\[3)\ a^{2} - 2ab + 5a - 10b =\]

\[= a(a - 2b) + 5 \cdot (a - 2b) =\]

\[= (a + 5)(a - 2b)\]

\[4)\ a^{3} - 3b + a^{2}b - 3a =\]

\[= a^{2}(a + b) - 3 \cdot (a + b) =\]

\[= (a + b)(a^{2} - 3)\]

\[5)\ a^{5} + 3a^{3} - 8a^{2} - 24 =\]

\[= a^{3}\left( a^{2} + 3 \right) - 8 \cdot \left( a^{2} + 3 \right) =\]

\[= \left( a^{3} - 8 \right)\left( a^{2} + 3 \right) =\]

\[= \left( a^{2} + 3 \right)(a - 2)\left( a^{2} + 2a + 4 \right)\]

\[6)\ a^{2} - 3a + b^{2} + 3b - 2ab =\]

\[= 3 \cdot (b - a) + b^{2} - 2ab + a^{2} =\]

\[= 3 \cdot (b - a) + (b - a)^{2} =\]

\[= (b - a)(3 + b - a)\ \]