Question 328244
Factor completely: 
{{{27+8t^3}}}
<pre><b>
What cubed is 27?
Answer; 3 cubed is 27, written {{{3^3}}}

What cubed is {{{8t^3}}}?
Don't know? Then break it down.
8 is 2 cubed and {{{t^3}}} is t cubed.

So write it this way

{{{(3)^3+(2t)^3}}}

Now the first part of the factorization is to write
the above down without the exponents:

{{{(3)+(2t)}}}

But take away the two inner parentheses and just make it

{{{(3+2t)}}}

The other parentheses will contain three terms, gotten this way:

Term 1:  Square the 3, get 9
Term 2:  Multiply the 3 by the 2t, getting 6t and change the sign, getting -6t
Term 3:  Square the (2t) getting {{{4t^2}}}

So the final factored form is:

{{{(3+2t)}}}{{{(9-6t+4t^2)}}}

Edwin</pre>