Factor completely 18a^2+60ab+50b^2?

I like the factoring by grouping
method:

Multiply the first coeffecient, 18, by
the last, 50 and we get 900.

We to find two numbers that
MULTIPLY to equal 900 and ADD to equal 60 (the middle
term)

We can use 30 and 30 because 30*30= 900 and 30+30
=60

Now we will rewrite 60ab as 30ab+30a giving
us

18a^2 + 30ab + 30ab
+50b^2

Group the first two and last two terms such
as

(18a^2 + 30ab) + (30ab
+50b^2)

Factor each set of () to
get

{6a(3a+5b)}
+{10(3a+5b)}

Notice that we have a (3a+5b in each set of
{}, so we can factor that out and
get

{6a+10b}(3a+5b)

we can
continue to factor {6a+10b}
as

2{3a+5b}(3a+5b)

Now we can
rewrite {3a+5b}(3a+5b) using an exponent to get our final answer
of

2(3a+5b) ^ 2