вправа 683 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) (a + 6)³ - 27 =
= ((a + 6) - 3)((a + 6)² +
+ 3(a + 6) + 9) =
= (a + 3)(a² + 12a +
+ 36 + 3a + 18 + 9) =
= (a + 3)(a² + 15a + 63);
2) (2x - 1)³ + 64 =
= ((2x - 1) + 4)((2x - 1)² -
- 4(2x + 1) + 16) =
= (2x + 3)(4x² - 4x +
+ 1 - 8x - 4 + 16) =
= (2x + 3)(4x² - 12x + 13); \begin{equation}3)8a^{6}-( 4a-3 )^{3}=\end{equation} \begin{equation}=( 2a^{2}-( 4a-3 ) )\end{equation} \begin{equation}( 4a^{4}+2a^{2}( 4a-3 )+\end{equation} \begin{equation}+( 4a-3 )^{2} )=\end{equation} \begin{equation}= ( 2a^{2}-4a+3 )\end{equation} \begin{equation} ( 4a^{4}+8a^{3}-6a^{2}+\end{equation} \begin{equation}+16a^{2}-24a+9 )=\end{equation} \begin{equation}= ( 2a^{2}-4a+3 )\end{equation} \begin{equation}( 4a^{4}+8a^{3}+10a^{2}-24a+9 );\end{equation} 4) 1000 + (y - 10)³ =
= (10 + (y - 10))(100 -
- 10(y - 10) + (y - 10)²) =
= y(100 - 10y + 100 +
+ y² - 20y + 100) =
= y(y² - 30y + 300);
5) (x + y)³ - (x - y)³ =
= ((x + y) - (x - y))((x + y)² +
+ (x + y)(x - y) + (x - y)²)=
= 2y(x² + 2xy + y² + x² -
- y² + x² - 2xy + y²) =
= 2y(3x² + y²);
6) (a - 2)³ + (a + 2)³ =
= ((a - 2) + (a + 2))((a - 2)² -
- (a - 2)(a + 2) + (a + 2)²) =
= 2a(a² - 4a + 4 - a² +
+ 4 + a² + 4a + 4) =
= 2a(a² + 12).