You got it! I am assuming that 12x*3y is really 12x^3y, since most factoring problems don't start with 12x * 3y. Two things to do if you want to check a factoring problem:
1) Multiply it out to see if you can get your original answer:
4xy * (3x^2 - 2y)
4xy * 3x^2 + 4xy * -2y
12 x^3 * y + -8 * x * y^2
12x^3y - 8xy^2
2) Look at each factor and make sure you can't do anything more:
4xy: Can't factor that! (Well, 4 * x * y, but that's silly.)
3x^2 - 2y: The first term has factors of 3, x, and x. The second term has factors of 2 and y. Since 3 and 2 are both prime, they obvoiusly have no factors in common. And no variables are in common either, so you're done!
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You got it! I am assuming that 12x*3y is really 12x^3y, since most factoring problems don't start with 12x * 3y. Two things to do if you want to check a factoring problem:
1) Multiply it out to see if you can get your original answer:
4xy * (3x^2 - 2y)
4xy * 3x^2 + 4xy * -2y
12 x^3 * y + -8 * x * y^2
12x^3y - 8xy^2
2) Look at each factor and make sure you can't do anything more:
4xy: Can't factor that! (Well, 4 * x * y, but that's silly.)
3x^2 - 2y: The first term has factors of 3, x, and x. The second term has factors of 2 and y. Since 3 and 2 are both prime, they obvoiusly have no factors in common. And no variables are in common either, so you're done!
I think you mean 12x^3y - 8xy^2 and not 12x*3y - 8xy*2. There's a big difference between the two.
So if you have this then 12x^3y - 8xy^2 then divide by 4 because that's our first common factor if we do that we get this:
4(3x^3y - 2xy^2), we notice here that both terms have a x and a y in them so we can pull those out too
4xy(3x^2 - 2y), this can't be simplified any further.
As we see now that you were right all along :D
its 4xy - 16xy which is -12xy