Question

Factory 12a^2 + 12ab+ 3b^2

Answer 1

Sorry, I've never heard of a factory with such name.

On a totally unrelated note, if you want to factor \(12a^2+12ab+3b^2\), then you could observe that \(3(2a+b)^2\) will yield the same expression.

Sorry for going a little off topic with that paragraph above.\[\]

Answer 2

She knows.

Answer 3

whats the confusion about then :o

Answer 4

lol, across!

Answer 5

I can show you another way to factored this without using trial factors if you like.

Answer 6

She didn't know what you meant about the term factory.
There is a mathematical term factor

Answer 7

Well she did know.

Answer 8

She was just making a little joke.

Answer 9

nd sure.. i just hate factoring polynomials

Answer 10

Factory is not a mathematical term.

Answer 11

OH WOW it was a typo
my bad

Answer 12

LOL haha

Answer 13

lol

Answer 14

anyway can u help me through this ?

Answer 15

Sure.

Answer 16

myin lies :P http://mathfactory.org/ is completely mathematics :D

Answer 17

Lol

Answer 18

12a^2 + 12ab+ 3b^2
So we have this and this means
\[12a^2+12ab+3b^2\]
The GCF of 12,12,3 is 3

So we have \[3(4a^2+4ab+b^2)\]
Now lets just look at the inside which is
\[4a^2+4ab+b^2 \text{ note : we will need \to bring that 3 down later }\]


\[4\cdot a^2+4b \cdot a+b^2\]

The trick is to find two factors of A*C that have product A*C and have sum B.

A=4 , B=4b , C=b^2

A*C=4b^2=2b*2b
and
B=4b=2b+2b

So now remember our middle term was 4b*a
and we have above 4b=2b+2b
so 4b*a=(2b+2b)*a=2ab+2ab

So we need to replace our middle term 4ab with 2ab + 2ab and then factor by grouping
\[4a^2+2ab+2ab+b^2\]
The first two terms have 2a in common
so we have
\[2a(2a+b)+2ab+b^2\]
The last two terms have b in common
so we have
\[2a(2a+b)+b(2a+b)\]
Now we have two terms and they both have (2a+b) in common so we can factor that out leaving us with
\[(2a+b)(2a+b)\]
We can also write this as
\[(2a+b)^2\]
Don't forget about the 3 we were suppose to bring down.

\[3(2a+b)^2\]

Answer 19

thanks this is so much better then just getting the answer

Answer 20

Well with experience some of these will become easier for you to just give the answer.