Question 185775
Not sure if this is in the right area. But the problem says" Factor the following expression." 
The problems is as follows: 
<pre><font size = 4 color = "indigo"><b>

{{{(x-2y)^3 - (x+4)^3}}}

You have to learn this set of rules:

{{{A^3+B^3=(A+B)(A^2-AB+B^2)}}}
{{{A^3-B^3=(A-B)(A^2+AB+B^2)}}}

In the second one, 

{{{A^3-B^3=(A-B)(A^2+AB+B^2)}}},

substitute {{{(x-2y)}}} for {{{A}}}, and {{{(x+4)}}} for {{{B}}}:

{{{(x-2y)^3-(x+4)^3=((x-2y)-(x+4))((x-2y)^2+(x-2y)(x+4)+(x+4)^2)}}}

Then remove the inner parentheses on the right:

{{{(x-2y)^3-(x+4)^3=(x-2y-x-4)(x^2-4xy+4y^2+x^2+4x-2xy-8y+x^2+8x+16)}}}

{{{(x-2y)^3-(x+4)^3=(-2y-4)(x^2-4xy+4y^2+x^2+4x-2xy-8y+x^2+8x+16)}}}

Factor -2 out of the first parentheses.  Combine like terms in
the second parentheses.

{{{(x-2y)^3-(x+4)^3=-2(y+2)(3x^2-6xy+4y^2+12x-8y+16)}}}

Edwin</pre>