Would anyone be able to factor this with work?

a^2 + 10ab + 25b^2 - c^2

Question

Would anyone be able to factor this with work? 

a^2 + 10ab + 25b^2 - c^2

cruffo · Answer

It looks like a difference of squares :)

anonymous · Answer

what was the formula again? (a^2-b^2) =?

cruffo · Answer

Right: a^2 - b^2 = (a+b)(a-b)

anonymous · Answer

right, so would i just pair each term? like a^2 + 10ab?

cruffo · Answer

Consider factoring the first part 

a^2 + 10ab + 25b^2 = (a + 5)^2

anonymous · Answer

oh thats right, sorry, im just a bit rusty

cruffo · Answer

Sorry, missed the b didn't I :)
a^2 + 10ab + 25b^2 = (a + 5b)^2

anonymous · Answer

thanks for the assistance, i greatly appreciate it, both of you

anonymous · Answer

just making sure, how do i know where to add the c?

anonymous · Answer

would i just follow the formula

cruffo · Answer

@cornitodisc is using "factoring by grouping"  I was thinking that by factoring the first part you could have a difference of squares:
(a+5b)^2 - c^2 = (a+5b + c)(a+5b - c)

anonymous · Answer

thats the right answer according to my teacher, when i looked at it the first time however, i was trying to break it into two groups. i didnt know what to do after i saw that 25b^2 and c^2 didnt have a common factor...

cruffo · Answer

I would say that usually when you see 4 terms factoring by breaking it up into two groups would be the first thing to try.  The extra letters, and the particular numbers gave me the idea to do it using another method.

anonymous · Answer

i wouldnt have been able to see that haha

cruffo · Answer

Let me see...

(a^2 + 10ab )  +   (25b^2 - c^2)

factor an a out of the first group:
a(a+10b) +  (25b^2 - c^2)
There is no common factor in the second group,
but it does fit the pattern x^2 - y^2, so
a(a+10b) + (5b + c)(5b - c)

anonymous · Answer

ah,,i see,,sorry

anonymous · Answer

its ok, ty for the input

cruffo · Answer

Yah, I don't see how to continue from here.

anonymous · Answer

lol thats what stumped me

cruffo · Answer

It's all the extra letters!!!

What I saw was the  "perfect square trinomial" a^2 + 10ab + 25b^2, 
so I knew that part factored to (something)^2.
Then I saw the "(something)^2-c^2" and thought "difference of squares"...

anonymous · Answer

I get it, haha, factoring is such a pain to me, thanks for the assistance!

cruffo · Answer

Cool!  Thank you!

anonymous · Answer

:D