Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1552

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\[1)\ y = (2x + 1)^{2} \bullet \sqrt{x - 1};\]

\[= (8x + 4) \bullet \sqrt{x - 1} + \frac{(2x + 1)^{2}}{2\sqrt{x - 1}} =\]

\[= \frac{2(8x + 4)(x - 1) + (2x + 1)^{2}}{2\sqrt{x - 1}} =\]

\[= \frac{16x^{2} - 16x + 8x - 8 + 4x^{2} + 4x + 1}{2\sqrt{x - 1}} =\]

\[= \frac{20x^{2} - 4x - 7}{2\sqrt{x - 1}}.\]

\[2)\ y = x^{2} \bullet \sqrt[3]{(x + 1)^{2}};\]

\[= \frac{2x \bullet 3(x + 1) + x^{2} \bullet 2}{3\sqrt[3]{x + 1}} =\]

\[= \frac{6x^{2} + 6x + 2x^{2}}{3\sqrt[3]{x + 1}} = \frac{8x^{2} + 6x}{3\sqrt[3]{x + 1}} =\]

\[= \frac{2x(4x + 3)}{3\sqrt[3]{x + 1}}.\]