Josalynn

2021-10-22

To calculate:
To factor the expression $\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}$.

Obiajulu

Calculation:
This can be written as
$\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}=2\cdot \frac{2}{3}\cdot {x}^{\frac{1}{3}}\cdot \left(2x-3\right)+2\cdot {x}^{\frac{1}{3}}\cdot x$
Factoring out the common terms i.e. 2 and ${x}^{\frac{1}{3}}$
$\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}=2\cdot {x}^{\frac{1}{3}}\cdot \left(\frac{2}{3}\left(2x-3\right)+x\right)$
$\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}=2{x}^{\frac{1}{3}}\left(\frac{2}{3}\cdot 2x-\frac{2}{3}\cdot 3+x\right)$
$\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}=2{x}^{\frac{1}{3}}\left(\frac{4x}{3}-\frac{6}{3}+x\right)$
$\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}=2{x}^{\frac{1}{3}}\left(\frac{4x}{3}-\frac{6}{3}+\frac{3x}{3}\right)$
$\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}=2{x}^{\frac{1}{3}}\left(\frac{7x}{3}-\frac{6}{3}\right)$
$\frac{4}{3}{x}^{\frac{1}{3}}\left(2x-3\right)+2{x}^{\frac{4}{3}}=2{x}^{\frac{1}{3}}\left(\frac{7x-6}{3}\right)$

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