Question 1058721
<pre><b>
I'll put in every step.  You can skip some.  Also
I won't bother to simplify the 2nd term, since you're
only interested in the 3rd term:

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
((8x)^(1/3)(-y)^0)/0!^""^"",
""+"",
((1/3)*(8x)^((1/3-1))*(-y)^1)/1!^""^"",
""+"",
(1/3)(1/3-1)(8x)^((1/3-2))*(-y)^2/2!^""^"",
""+"",
""*""*""*""




)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
(8^(1/3)*x^(1/3)(1))/1^""^"",
""+"",
((1/3)*(8x)^((1/3-3/3))*(-y))/1^""^"",
""+"",
(1/3)(1/3-3/3)(8x)^((1/3-3/3))*y^2/2^""^"",
""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""+"",
((1/3)(-2/3)(8x)^(-2/3)*y^2)/2^""^"",
""+"",
""*""*""*""

)}}}


{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""+"",
((-2/9)(8x)^(-2/3)*y^2)/2^""^"",
""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
((2/9)(8x)^(-2/3)*y^2)/2^""^"",
""+"",
""*""*""*""

)}}}


{{{matrix(2,13,"","","","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
((2/9)(8x)^(-2/3)*y^2),
"÷",
2,
""+"",
""*""*""*""

)}}}

{{{matrix(2,13,"","","","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
((2/9)(8x)^(-2/3)*y^2),
""*"",
1/2,
""+"",
""*""*""*""

)}}}

{{{matrix(2,13,"","","","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
((cross(2)/9)(8x)^(-2/3)*y^2),
""*"",
1/cross(2),
""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
((1/9)(8x)^(-2/3)*y^2),

""+"",
""*""*""*""

)}}}

{{{matrix(2,13,"","","","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
((8x)^(-2/3)*y^2),
"÷",
9,

""+"",
""*""*""*""

)}}}

{{{matrix(2,13,"","","","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
(y^2^""/(8x)^(2/3)^""),
""*"",
1/9,

""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
y^2^""/(9(8x)^(2/3)^""),


""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
y^2^""/(9*8^(2/3)*x^(2/3)^""),


""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
y^2^""/(9*(root(3,8))^2*x^(2/3)^""),


""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
y^2^""/(9*(2)^2*x^(2/3)^""),


""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
y^2^""/(9*4*x^(2/3)^""),


""+"",
""*""*""*""

)}}}

{{{matrix(2,11,"","","","","","","","","","","",
(8x-y)^(1/3),
"",
""="",
"",
2*x^(1/3),
""-"",
(1/3)*(8x)^(-2/3)*y,
""-"",
y^2^""/(36*x^(2/3)^""),


""+"",
""*""*""*""

)}}}

So the 3rd term simplified is


{{{

-y^2^""/(36*x^(2/3)^"") }}}

Edwin</pre></b>