Question

Can someone explain how to do this so I understand?
Factor completely: −6x3y + 9x2y2 − 12xy3

Answer 1

Look at numbers 6, 9, and 12.
Do they have a common factor?

Answer 2

3?
if that's what you mean

Answer 3

yes

Answer 4

Now look at x^3, x^2 and x.
Do they have a common factor?

Answer 5

uhm.. x??

Answer 6

yes, again. good job so far.
third q: what is the common factor of y, y^2, y^3?

Answer 7

y

Answer 8

good.
Now you know you are going to factor out
3xy, so your answer will look like
3xy( )

Answer 9

Now look again at the original polynomial.
−6x3y + 9x2y2 − 12xy3 = 3xy( )
We need to fill in the parentheses.

Answer 10

Let's work on one term of the original polynomial at a time.
What do you multiply 3xy by to get -6x^3y? In other words what is -6x^3y/3xy?

Answer 11

-2x^2y?

Answer 12

Almost. No need for y, since you have a y in 3xy, and you need to end up with -6x^3y which also only has y, not y^2.
So it's -2x^2

Answer 13

We're here now:
3xy(-2x )
Next term is 9x^2y^2
What do you multiply 3xy by to get 9x^2y^2? In other words, what is 9x^2y^2/3xy?

Answer 14

3xy?

Answer 15

Would it be 3xy(−2x2 + 3xy − 4y2) ??

Answer 16

correct

Answer 17

Good job!

Answer 18

Awesome ! Thank you soo much !! You made it much easier than it seems !!

Answer 19

wlcm

Answer 20

This kind of factoring is using the distributive property in reverse.