# How do you simplify ( 1 + x^(4/3) ) x ( 1 - x^(2/3) )?

Nov 13, 2015

$x \left(1 - {x}^{\frac{2}{3}}\right)$

#### Explanation:

Multiply the last bracket by the $x$ that is between:

$\left(1 + {x}^{\frac{4}{3}}\right) \left(x - {x}^{\frac{5}{3}}\right)$

Note that ${x}^{b} \times {x}^{c} = {x}^{b + c}$

Also that $x \times {x}^{\frac{4}{3}} = {x}^{\frac{4}{3} + 1} = {x}^{\frac{4}{3} + \frac{3}{3}} = {x}^{\frac{7}{3}}$

Expanding brackets

$x - {x}^{\frac{5}{3}} + {x}^{\frac{7}{3}} - {x}^{\frac{7}{3}}$

but $+ {x}^{\frac{7}{3}} - {x}^{\frac{7}{3}} = 0$

$x \left(1 - {x}^{\frac{2}{3}}\right)$