(1+√(x^3 )) 〖(x〗^(-3)-2∛x )

asked by guest
on Jan 22, 2025 at 8:58 am



You asked:

Evaluate the expression: \(\left(1 + \sqrt{{x}^{3}}\right) \left({x}^{-3} - 2 \sqrt[3]{x}\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(1 + \sqrt{{x}^{3}}\right) \left({x}^{-3} - 2 \sqrt[3]{x}\right) = \left(- 2 \sqrt[3]{x} + \frac{1}{x^{3}}\right) \left(\sqrt{x^{3}} + 1\right) \)

Expanded

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

Factored

\[\left(1 + \sqrt{{x}^{3}}\right) \left({x}^{-3} - 2 \sqrt[3]{x}\right) = - \frac{\left(2 x^{\frac{10}{3}} - 1\right) \left(\sqrt{x^{3}} + 1\right)}{x^{3}}\]

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