Question 234171
factor completely:
{{{8x^4y^4-18x^2y^6}}}
<pre><font size = 4 color = "indigo"><b>
Look for the largest whole number you can factor out of 8 and 18.
This is 2.

Now look for the LARGEST power of x you can factor out.  This is
the SMALLEST power that occurs, but x must appear in ALL terms.
This is {{{x^2}}}


Now look for the LARGEST power of y you can factor out.  This is
the SMALLEST power that occurs, but y must appear in ALL terms.
This is {{{y^4}}}

So factor out {{{2x^2y^4}}}

{{{2x^2y^4(4x^2-9y^2)}}}

Now the expression in parentheses is the difference of two
perfect squares. {{{4x^2}}} is the same as {{{(2x)^2}}} and
{{{9y^2}}} is the same as {{{(3y)^2}}} so that expression in
parentheses factors as the sum of times difference of the bases
of those perfect squares, i.e., their square roots:

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

Edwin</pre>