Решебник по алгебре 7 класс Мерзляк ФГОС Задание 713

 

\[\boxed{\text{713\ (713).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 4a³ - 4b^{3} = 4 \cdot \left( a^{3} - b^{3} \right) =\]

\[= 4 \cdot (a - b)(a^{2} + \text{ab} + b^{2})\]

\[2)\ 2m³ - 16 = 2 \cdot \left( m^{3} - 8 \right) =\]

\[= 2 \cdot (m - 2)(m^{2} + 2m + 4)\]

\[3)\ 7 + 7b³ = 7 \cdot \left( 1 + b^{3} \right) =\]

\[= 7 \cdot (1 + b)(1 - b + b^{2})\]

\[4) - x^{4} + 27x = x\left( 27 - x^{3} \right) =\]

\[= x(3 - x)(9 + 3x + x^{2})\]

\[5)\ 2a^{4} - 250a =\]

\[= 2a\left( a^{3} - 125 \right) =\]

\[= 2a(a - 5)(a^{2} + 5a + 25)\]

\[6)\ 9a^{5} - 9a^{2} = 9a^{2}\left( a^{3} - 1 \right) =\]

\[= 9a²(a - 1)(a^{2} + a + 1)\]

\[\boxed{\text{713.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ (x - 12)(x + 12) =\]

\[= 2 \cdot (x - 6)^{2} - x^{2}\]

\[x^{2} - 144 =\]

\[= 2 \cdot \left( x^{2} - 12x + 36 \right) - x^{2}\]

\[x^{2} - 144 =\]

\[= 2x^{2} - 24x + 72 - x^{2}\]

\[24x = 216\]

\[x = 9\]

\[Ответ:x = 9.\]

\[2)\ (3x - 1)^{2} + (4x + 2)^{2} =\]

\[= (5x - 1)(5x + 1)\]

\[10x = - 6\]

\[x = - 0,6\]

\[Ответ:\ x = - 0,6.\]

\[16x = - 80\]

\[x = - 5\]

\[Ответ:\ x = - 5.\]