Question

What is the GCF of 8x3y2 + 20x2y4?




4x2y2

4x3y4

4x3y4

2x2y2

Answer 1

that didn't help !!!!

Answer 2

@the_wiz_of_noobs

Answer 3

\[\large\rm 8x^3y^2 + 20x^2y^4\quad=\quad 8xxxyy+20xxyyyy\]It might be easier if we pick out the x's and y's first.
The first term has 3 x's, while the second term has 2 of them.
So they both have at least 2 x's, ya? :)\[\large\rm =xx(8xyyy+20yyyy)\]I took 2 x's out of each.
Follow so far?

Answer 4

How many y's can you pull out of each?

Answer 5

you can take away 2 y's

Answer 6

Hmm the first term has 3,
the second term has 4,
so they both have at least 3 y's, ya? :)

Answer 7

i didn't see the 3 y's !! but ok. You can take away 3 y's.

Answer 8

\[\large\rm =xxyyy(8x+20y)\]Hmm ok, and then we should do something about this 8 and 20.

Answer 9

Notice they're both even numbers,
so they both have a 2 in them.
Maybe more though.

Answer 10

We could break them down like we did with the x and y's.

Answer 11

wouldn't we evaluate ?? or no ??

Answer 12

\[\large\rm =xxyyy(4\cdot2x+4\cdot5y)\]I rewrote the 8 as 4*2,
and the 20 as 4*5.

Answer 13

evaluate? I'm not sure what you mean.

Answer 14

idk, im new at this.. cause if you have (8+20) then i thought you would evaluate that but that wouldnt make since .. cause that would be 28.. and that don't go with this problem forget that i said that!!!

Answer 15

:D

Answer 16

Ok so all I did was rewrite the 8 and 20 in clever ways.
Hmm they both have a 4 in them, yes?

Answer 17

yes.

Answer 18

\[\large\rm =4xxyyy(2x+5y)\]Ok cool we'll take the 4 out.

Answer 19

From here, we can see that the two things in the brackets no longer share anything in common.

So bam we're done.\[\large\rm =4x^2y^3(2x+5y)\]The GCF is the stuff that we pulled outside of the brackets.

Answer 20

That's not one of our options though :)
Hmm sec, I think I made a boo boo

Answer 21

There was only supposed to be 2 y's in the first one,
just like you said hehe

sorry about that :(
so we end up with 1 less y outside,
and one more y inside on the second term.\[\large\rm =4x^2y^2(2x+5y^2)\]