Решебник по алгебре 7 класс Мерзляк ФГОС Задание 709

 

\[\boxed{\text{709\ (709).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 3a² + 6\text{ab} + 3b² =\]

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

\[= 3 \cdot (a + b)²\]

\[2)\ 5m² + 5n² - 10\text{mn} =\]

\[= 5 \cdot \left( m^{2} - 2mn + n^{2} \right) =\]

\[= 5 \cdot (m - n)²\]

\[3) - 3x^{2} + 12x - 12 =\]

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

\[= - 3 \cdot (x - 2)²\]

\[4) - 7b^{2} - 14bc - 7c^{2} =\]

\[= - 7 \cdot \left( b^{2} + 2bc + c^{2} \right) =\]

\[= - 7 \cdot (b + c)²\]

\[5)\ x²y + 14xy² + 49y³ =\]

\[= y\left( x^{2} + 14xy + 49y^{2} \right) =\]

\[= y(x + 7y)²\]

\[6) - 8a^{3}b + 56a^{2}b^{2} - 98ab^{3} =\]

\[= - 2ab\left( 4a^{2} - 28ab + 49b^{2} \right) =\]

\[= - 2ab(2a - 7b)²\]

\[\boxed{\text{709.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \left( 0,02p^{3}k + 20p^{2}k^{4} \right)^{2} =\]

\[2)\ \left( 1\frac{1}{6}mn - \frac{4}{21}m^{2}n^{5} \right)^{2} =\]

\[= \left( \frac{7}{6}mn - \frac{4}{21}m^{2}n^{5} \right)^{2} =\]

\[3) - 15 \cdot \left( \frac{1}{3}a - \frac{1}{5}b \right)^{2} =\]

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

\[= - 1\frac{2}{3}a^{2} + 2ab - \frac{3}{5}b^{2}\]

\[4)\ 7x\left( x^{3} - 2x \right)^{2} =\]

\[= 7x\left( x^{6} - 4x^{4} + 4x^{2} \right) =\]

\[= \ 7x^{7} - 28x^{5} + 28x^{3}\]

\[5)\ (5y - 2)^{2}(2y + 1) =\]

\[= \left( 25y^{2} - 20y + 4 \right)(2y + 1) =\]

\[= 50y^{3} - 15y^{2} - 12y + 4\]

\[6)\ (10p - k)^{2}(10p + k)^{2} =\]

\[= \left( (10p - k)(10p + k) \right)^{2} =\]

\[= \left( 100p^{2} - k^{2} \right)^{2} =\]

\[= 10\ {000p}^{4} - 200p^{2}k^{2} + k^{4}\]