вправа 707 гдз 7 клас алгебра Мерзляк Полонський

Відповідь:

1) 2a² - 2b² = 2(a² - b²) =
= 2(a - b)(a + b);
2) cx² - cy² = c(x² - y²) =
= c(x - y)(x + y);
3) 3x² - 3 = 3(x² - 1) =
= 3(x - 1)(x + 1);
4) 3ab² - 27a = 3a(b² - 9) =
= 3a(b - 3)(b + 3);
5) x³ - 4x = x(x² - 4) =
= x(x - 2)(x + 2);
6) 2y³ - 18y = 2y(y² - 9) =
= 2y(y - 3)(y + 3); \begin{equation}7)x^{4}-x^{2}=x^{2}\left ( x^{2}-1 \right )=\end{equation} \begin{equation}=x^{2}\left ( x-1 \right )\left ( x+1 \right );\end{equation} \begin{equation}8)0,09t^{4}-t^{6}=\end{equation} \begin{equation}=t^{4}\left ( 0,09-t^{2} \right )=\end{equation} \begin{equation}=t^{4}\left ( 0,3-t \right )\left ( 0,3+t \right );\end{equation} \begin{equation}9)\frac{16}{49}a^{2}b^{4}c^{5}-b^{2}c^{3}=\end{equation} \begin{equation}=b^{2}c^{3}\left ( \frac{16}{49}a^{2}b^{2}c^{2}-1 \right )=\end{equation} \begin{equation}=b^{2}c^{3}\left ( \frac{4}{7}abc-1 \right )\left ( \frac{4}{7}abc+1 \right ).\end{equation}