вправа 540 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) (x + 2)² - 49 = (x + 2 - 7)(x + 2 + 7) =
= (x - 5)(x + 9);
2) (x - 10)² - 25y² =
= (x - 10 - 5y)(x - 10 + 5y);
3) 25 - (y - 3)² =
= (5 - (y - 3))(5 + (y - 3)) =
= (8 - y)(2 + y);
4) (a - 4)² - (a + 2)² =
= ((a - 4) - (a + 2))((a -
- 4) + (a + 2)) =
= -6(2a - 2) = -12(a - 1);
5) (m - 10)² - (n - 6)² =
= ((m - 10) - (n - 6))((m -
- 10) + (n - 6)) =
= (m - n - 4)(m + n - 16);
6) (8y + 4)² - (4y - 3)² =
= ((8y + 4) - (4y - 3))((8y +
+ 4) + (4y - 3)) =
= (4y + 7)(12y + 1);
7) (5a + 3b)² - (2a - 4b)² =
= ((5a + 3b) - (2a - 4b))((5a +
+ 3b) + (2a - 4b)) =
= (3a + 7b)(7a - b);
8) 4(a - b)² - (a + b)² =
= (2(a - b) - (a + b))(2(a -
- b) + (a + b)) =
= (a - 3b)(3a - b);
9) (x² + x + 1)² - (x² - x + 2)² =
= ((x² + x + 1) - (x² - x + 2))((x² +
+ x + 1) + (x² - x + 2)) =
= (2x - 1)(2x² + 3); \begin{equation}10)\left ( -3x^{3}+y \right )^{2}-16x^{6}=\end{equation} \begin{equation}=\left ( \left ( -3x^{3}+y \right )-4x^{3} \right )\end{equation} \begin{equation}\left ( \left ( -3x^{3}+y \right )+4x^{3} \right )=\end{equation} \begin{equation}=\left ( y-7x^{3} \right )\left ( y+x^{3} \right ).\end{equation}