I need a full explanation, I was lazy with this part of the lesson :3

Identify the GCF of 8x4y4 − 24x3y3 + 16x3y2.

Question

I need a full explanation, I was lazy with this part of the lesson :3

Identify the GCF of 8x4y4 − 24x3y3 + 16x3y2.

ja1 · Answer

I just need to know how to get it

espex · Answer

You just need to find the largest number/variable combination that will go into all of those terms.

ja1 · Answer

Yes but I couldn't find any off the bat... one sec

ja1 · Answer

4x3y2

 8x3y2

 8x2y3

 4xy

ja1 · Answer

I know for a fact B and C are not it right?

espex · Answer

Start with the integers, what is the largest number that will go into 8, 24, and 16?

ja1 · Answer

Well 8 x 1 = 8 8 x 3 - 24 and 8 x 2 - 16 so 8

ja1 · Answer

Florida
Polk County

ja1 · Answer

my bad wrong place xD

espex · Answer

Okay, now what is the largest power of 'x' that will go into x^4, x^3, and x^3?
What is the largest power of 'y' that will go into y^4, y^3, and y^2?

ja1 · Answer

1 for both right?

espex · Answer

No, maybe think of the exponents as addition. For example, x^4 is x^(2+2) or x^(3+1)

espex · Answer

When you divide you are "subtracting" your powers.

ja1 · Answer

OH right i forgot >_<

ja1 · Answer

so it would be 3 and 2?

espex · Answer

Exactly, put it all together and you have your answer.

ja1 · Answer

but how does 3+2 = 4?

espex · Answer

It doesn't.

ja1 · Answer

So you just pick the highest possible number that when added to any other number equals the X and Y exponents?

ja1 · Answer

Like 3 + Anything = all exponents?

espex · Answer

Let's look at your 'x', you have exponents of 4, 3, and 3. What is the highest number can you subtract from all of them?

ja1 · Answer

Ah ok so you just pick the highest number that goes into all of them so if the example was 8  
4 and 4 the GCF would be 4?

espex · Answer

If we are talking about integers, and you had 8 and 4, then the GCF would be 4. If we are talking about exponents, and you have 5 and 4, then the GCF would be 4. With integers it is the largest number that will divide into both numbers, with exponents it is the largest number you can subtract from both exponents.

ja1 · Answer

Ah yes well thank you so much, I hadn't even looked at this par of the lesson thanks I understand it now :)

espex · Answer

You're welcome.