вправа 400 гдз 7 клас алгебра Мерзляк Полонський
7 клас ➠ алгебра ➠ Мерзляк Полонський
Вправа 400
Відповідь:
1) (x + 2)(x - 1)(x - 4) =
= (x + 2)(x² - 5x + 4) =
= x³ - 5x² + 4x + 2x² - 10x + 8 =
= x³ - 3x² - 6x + 8;
2) (2x + 1)(x + 5)(x - 6) =
= (2x + 1)(x² - x - 30) =
= 2x³ - 2x² - 60x + x² - x - 30 =
= 2x³ - x² - 61x - 30; \begin{equation}3)\left ( x^{2} -2x+3\right )\left ( x^{2}+2x-3 \right )=\end{equation} \begin{equation}=x^{4}+2x^{3}-3x^{2}-2x^{3}-\end{equation} \begin{equation}-4x^{2}+6x+3x^{2}+6x-9=\end{equation} \begin{equation}=x^{4}-4x^{2}+12x-9;\end{equation} 4) (a + 2b - c)(a - 3b + 2c) =
= a² - 3ab + 2ac + 2ab -
- 6b² + 4bc - ac + 3bc - 2c² =
= a² - 6b² - 2c² - ab + ac + 7bc; \begin{equation}5)\left ( a+b \right )\left ( a^{3}-a^{2}b+ab^{2}-b^{3} \right )=\end{equation} \begin{equation}=a^{4}-a^{3}b+a^{2}b^{2}-ab^{3}+a^{3}b-\end{equation} \begin{equation}-a^{2}b^{2}+ab^{3}-b^{4}=\end{equation} \begin{equation}=a^{4}-b^{4}.\end{equation}
1) (x + 2)(x - 1)(x - 4) =
= (x + 2)(x² - 5x + 4) =
= x³ - 5x² + 4x + 2x² - 10x + 8 =
= x³ - 3x² - 6x + 8;
2) (2x + 1)(x + 5)(x - 6) =
= (2x + 1)(x² - x - 30) =
= 2x³ - 2x² - 60x + x² - x - 30 =
= 2x³ - x² - 61x - 30; \begin{equation}3)\left ( x^{2} -2x+3\right )\left ( x^{2}+2x-3 \right )=\end{equation} \begin{equation}=x^{4}+2x^{3}-3x^{2}-2x^{3}-\end{equation} \begin{equation}-4x^{2}+6x+3x^{2}+6x-9=\end{equation} \begin{equation}=x^{4}-4x^{2}+12x-9;\end{equation} 4) (a + 2b - c)(a - 3b + 2c) =
= a² - 3ab + 2ac + 2ab -
- 6b² + 4bc - ac + 3bc - 2c² =
= a² - 6b² - 2c² - ab + ac + 7bc; \begin{equation}5)\left ( a+b \right )\left ( a^{3}-a^{2}b+ab^{2}-b^{3} \right )=\end{equation} \begin{equation}=a^{4}-a^{3}b+a^{2}b^{2}-ab^{3}+a^{3}b-\end{equation} \begin{equation}-a^{2}b^{2}+ab^{3}-b^{4}=\end{equation} \begin{equation}=a^{4}-b^{4}.\end{equation}