Question

Factor completely.

Answer 1

\[18x^3y-33x^2y^2-30xy^3\]

Answer 2

is there something that we could factor out of this?

Answer 3

maybe something that all the terms have in common?

Answer 4

yes the xy and hmm i guess the number 3?

Answer 5

very good, if we factor those out we will get: 3xy(6x^2-11xy-10y^2)

Answer 6

now, we have to see if that quadratic onnthe inside can be factored, what do you think?

Answer 7

hmmm im not sure i thought 2 but that is wrong.

Answer 8

3xy(6x^2-11xy-10y^2)

Well, we can use a bit of guess and check: lets say we start off with: (3x+?)(2x+?), since these two particular terms well give us 6x^2 okay

Answer 9

ok got it so far

Answer 10

Sorry, one of them has to have a minus sign,now (3x+?)(2x-?)=6x^2-3x?+2x?-?^2

Answer 11

now, the reason i did all of that is because we need to find numbers that will give us what we want, namely 6x^2-11xy-10y^2

Answer 12

So what we factor with has to have a minus sign?

Answer 13

yes, because if you notice the orginal quadratic has :6x^2-11xy-10y^2, it has two minus signs. So we need a minus sign in one of our terms. Now let me as you what comnbination of number well give us -10y^2

Answer 14

thats i to say, what numbers when ,multiplied together give us -10y^2

Answer 15

hmmm -2 and 5? right?

Answer 16

yes, in fact it s -2y and 5y, right, since we also want that y^2 part

Answer 17

oh yeah sorry forgot that part.

Answer 18

now we have (3x+?,)(2x-?), but we have found the numbers that should replace the quetion marks, can you postion those numbers so that we get: 6x^2-11xy-10y^2

Answer 19

so wait is it 3x-2 and 2x+5?

Answer 20

well, remeber we found the two numbers to be 2y and 5y

Answer 21

oh yeah so 2y and 5y sorry haha

Answer 22

so, now you are saying that it should be : (3x-2y) and (2x+5y), does, that when you multiply it our, give you 6x^2-11xy-10y^2

Answer 23

i think so cause 3*2=6 and -2*5=-10 and how do you get the 11xy

Answer 24

its from the two middle terms

Answer 25

oh yeah forgot bout foil

Answer 26

now, you have the correct terms. But just make sure you get the result you want.

Answer 27

the answer should look something like this ?xy(?x+?y)(?x-?y)

Answer 28

The answer, when completlely, factored looks like this: 3xy(2x-5y)(3x+3y)

Answer 29

hmmm i got it wrong but i have 2 more tries i wonder what is wrong.

Answer 30

I got it wrong.