Simplify the expression (2x^3)/(x-4)(x^3-64)/(2x^2)

 Exercise

$\left(\frac{2x^3}{x-4}\right)\left(\frac{\left(x^3-64\right)}{2x^2}\right)$

 

Multiplying fractions $\frac{2x^3}{x-4} \times \frac{x^3-64}{2x^2}$

$\frac{2x^3\left(x^3-64\right)}{2\left(x-4\right)x^2}$

 

Simplify the fraction $\frac{2x^3\left(x^3-64\right)}{2\left(x-4\right)x^2}$ by $2$

$\frac{x^3\left(x^3-64\right)}{\left(x-4\right)x^2}$

 

Simplify the fraction $\frac{x^3\left(x^3-64\right)}{\left(x-4\right)x^2}$ by $x$

$\frac{x\left(x^3-64\right)}{x-4}$

 

Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$

$\frac{x\left(x-4\right)\left(x^2+4x+16\right)}{x-4}$

 

Simplify the fraction $\frac{x\left(x-4\right)\left(x^2+4x+16\right)}{x-4}$ by $x-4$

$x\left(x^2+4x+16\right)$

$x\left(x^2+4x+16\right)$

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