Question 66007
{{{ 2x^4-54x }}}
factor out a 2x
{{{ 2x(x^3-27) }}}
look at the portion in the paranthesis.
{{{ x^3 - 27 }}}
This is the difference of two cubes.
There are 2 different "special patterns" to memorize here.
One for the sum of two cubes, the other for the difference of two cubes.
1. {{{ X^3+ Y^3 = (x + y)(X^2 - XY + Y^2) }}} 
2. {{{ X^3 -Y^3 = (X - Y)(X^2 + XY + Y^2) }}}
We are using the second formula/pattern
{{{ 2x(x^3-27) }}}
the cube root of x^3 = x
the cube root of 27 = 3
{{{ 2x (x - 3)(x^2+3x+9) }}}