Question 123271
<font size = 6 color = "red"><b> SCOTT'S IS RIGHT, BUT
STANBON'S IS WRONG BECAUSE HE FORGOT TO TAKE OUT 13.
HERE'S MY EXPLANATION.

BY EDWIN
</font>
How would you factor out the greatest common factor for this problem? 
{{{13y^8+26y^4-39y^2}}} 
Help would be much appreciated.
<pre>
You can do it shorter after you learn, but this 
is the best way to learn how.  Break everything
down into prime factors, so there are no exponents. 

13*y*y*y*y*y*y*y*y + 2*13*y*y*y*y - 3*13*y*y

Now I'll do some coloring:

<font color = "red">13*y*y</font><font color = "blue">*y*y*y*y*y*y</font> + <font color = "blue">2*</font><font color = "red">13*y*y</font><font color = "blue">*y*y</font> - <font color = "blue">3</font>*<font color = "red">13*y*y</font>

All three of those terms contain <font color = "red">13*y*y</font>.  So that's what
you can take out of each one, and what's left goes in the
parentheses:

So you put the common <font color = "red">red</font> part out front, and put the <font color = "blue">blue</font> part
inside a set of parentheses:

<font color = "red">13*y*y</font>(<font color = "blue">y*y*y*y*y*y + 2*y*y - 3</font>)

Then you simplify it by bringing the exponents back in:

13y<sup>2</sup>(y<sup>6</sup> + 2y<sup>2</sup> - 3)

Edwin</pre>