Question 191267
<pre><font size = 4 color = "indigo"><b>
{{{81a^2-27ab-18b^2}}}

First factor out {{{9}}}

{{{9(9a^2-3ab-2b^2)}}}

In the parentheses, multiply the first coefficient 9
by the last coefficient 2, getting 18.  Write down
all pairs of integer factors whose product is 18.
They are

1*18
2*9
3*6

Since the last sign in the parentheses is -, we
subtract those, larger minus smaller:

18-1 = 17
9-2 = 7
6-3 = 3


Since the middle coefficient of {{{(9a^2-3ab-2b^2)}}}
is 3, and since 3 = 6-3 we write -3ab as -6ab+3ab

{{{9(9a^2-6ab+3ab-2b^2)}}}

Factor the first two terms in the parentheses by factoring 
out {{{3a}}}

{{{9(3a(3a-2b)+3ab-2b^2)}}}
 
Factor the last two terms in the parentheses by factoring 
out {{{b}}}

{{{9(3a(3a-2b)+b(3a-2b))}}}

Inside the parentheses take out {{{(3a-2b)}}}

{{{9(3a-2b)(3a+b)}}}

Edwin</pre>