Question

So, I need help with this problem: 10x^4y^2z - 20x^3yz^3. I need to factor out the greatest common factor. I have already done so and gotten 10x^3yz for the first part. I need help with the second part. the full answer is either 10x^3yz(xy-2z^2) or 10x^3yz(2xyz-4xyz^2)

Answer 1

can you put in a screenshot, that looks so confusing to read like that

Answer 2

You're on the right track so far!

Answer 3

\( 10x^4y^2z - 20x^3yz^3\)

And \(10x^3yz \) is the GCF

Answer 4

The way to simplify it now is

Let's look at each individual term

\( 10x^4y^2z\) what are you left with when you factor out \(10x^3yz\)

Answer 5

yep.

Answer 6

what do you get

Answer 7

\( 10x^4y^2z\)

what are you left with when you factor out \(10x^3yz\)

Answer 8

xyz

Answer 9

oops are you sure there's a `z`?

Answer 10

Whoops my mistake

Answer 11

x and y

Answer 12

Yes! So now we have

\( 10x^3yz (xy) \)

Now what about the other term

\( 20x^3yz^3 \)
what do you get when you factor out \( 10x^3 yz\)

Answer 13

2z^2

Answer 14

so then it would be 10x^3yz(xy-2z^2)

Answer 15

Great!! So now we went from

\(10x^4y^2z- 20x^3yz^3 \)

to

\( 10x^3yz (xy) - 10x^3yz(2z^2) \)

Answer 16

That is correct!!!

Answer 17

Thank you for helping me.

Answer 18

And let me show you with some colors so you can remember it forever

\( \color{orange}{10x^3yz }(xy) - \color{orange}{10x^3yz}(2z^2) \)

if we think of \(10x^3yz\) as `a`

we have now
\( \color{orange}{a }(xy) - \color{orange}{a}(2z^2) \)


and NOW we can factor out `a and we get

\( \color{orange}{a }(xy- 2z^2) \)

and if we replace `a` back with our \( 10x^3yz\) we'll get

\( \color{orange}{10x^3yz}(xy- 2z^2) \)

Answer 19

Do you see it now?

Answer 20

Yes.

Answer 21

Great!