An expression is shown below:

2x3y + 18xy - 10x2y - 90y

1. Rewrite the expression so that the GCF is factored completely.

2. Rewrite the expression completely factored. Show the steps of your work.

3. If the two middle terms were switched so that the expression became 2x3y - 10x2y + 18xy - 90y, would the factored expression no longer be equivalent to your answer in part 2? Explain your reasoning.

Question

An expression is shown below:

2x3y + 18xy - 10x2y - 90y

1.  Rewrite the expression so that the GCF is factored completely.

2.  Rewrite the expression completely factored. Show the steps of your work.

3.  If the two middle terms were switched so that the expression became 2x3y - 10x2y + 18xy - 90y, would the factored expression no longer be equivalent to your answer in part 2? Explain your reasoning.

anonymous · Answer

$$2x^3y + 18xy - 10x^2y - 90y$$ right?

anonymous · Answer

common factor? each term has a $2y$ in it 
factor it out first

elise_a18 · Answer

yes that's correct

elise_a18 · Answer

i got 2y(9x^3-5x^2-45) for A. is that correct?  @satellite73

elise_a18 · Answer

@satellite73

anonymous · Answer

looks like you are missing something

anonymous · Answer

$$2x^3y + 18xy - 10x^2y - 90y$$ factor out the $2y$ and get 
$$2y(x^3+9x-5x^2-45)$$

anonymous · Answer

then  you can factor further, but how you are supposed to do that i am not sure

anonymous · Answer

final factored form is $$2 y(x-5) (x^2+9)$$

anonymous · Answer

maybe we can write 
$$x^3-5x^2+9x-45$$ as $$x^2(x-5)+9(x-5)$$ then we see a common factor of $x-5$ so factor further as 
$$(x^2-9)(x-5)$$

anonymous · Answer

as for 3) there is only one way to factor a polynomial, so nothing would change

elise_a18 · Answer

I completed it. Thanks for your help! I forgot to do that last step @satellite73