Решебник по алгебре 7 класс Мерзляк ФГОС Задание 843

 

\[\boxed{\text{843\ (843).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

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

\[= 16n^{2} + 8n + 1 - n^{2} - 8n - 16 =\]

\[= 15n^{2} - 15 =\]

\[= 15 \cdot \left( n^{2} - 1 \right) =\]

\[= 15 \cdot \underset{делится\ на\ 8}{\overset{(n - 1)(n + 1)}{︸}},\ \ \]

\[тогда\ 15 \cdot 8 = 120\ \ делится\ \]

\[на\ 120\ при\ любом\ нечетном\ \]

\[значении\ n.\]

\[\boxed{\text{843.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 2a² - 2b^{2} = 2 \cdot \left( a^{2} - b^{2} \right) =\]

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

\[2)\ \text{cx}² - cy^{2} = c\left( x^{2} - y^{2} \right) =\]

\[= c(x - y)(x + y)\]

\[3)\ 3x² - 3 = 3 \cdot \left( x^{2} - 1 \right) =\]

\[= 3 \cdot (x - 1)(x + 1)\]

\[4)\ 3ab² - 27a = 3a\left( b^{2} - 9 \right) =\]

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

\[5)\ x³ - 4x = x\left( x^{2} - 4 \right) =\]

\[= x(x - 2)(x + 2)\]

\[6)\ 2y³ - 18y = 2y\left( y^{2} - 9 \right) =\]

\[= 2y(y - 3)(y + 3)\]

\[7)\ x^{4} - x^{2} = x^{2}\left( x^{2} - 1 \right) =\]

\[= x²(x - 1)(x + 1)\]

\[8)\ 0,09t^{4} - t^{6} =\]

\[= t^{4}\left( 0,09 - t^{2} \right) =\]

\[= t^{4}(0,3 - t)(0,3 + t)\]

\[9)\frac{16}{49}a^{2}b^{4}c^{5} - b^{2}c^{3} =\]

\[= b^{2}c^{3}\left( \frac{16}{49}a^{2}b^{2}c^{2} - 1 \right) =\]

\[= b^{2}c^{3}\left( \frac{4}{7}abc - 1 \right)\left( \frac{4}{7}abc + 1 \right)\]