Question

Can someone help me please? :)
An expression is shown below:
2x^3y + 8xy - 4x^2y - 16y
Part A ~ Rewrite the expression so that the GCF is factored completely.
Part B ~ Rewrite the expression completely factored. Show the steps of your work.
Part C ~ If the two middle terms were switched so that the expression became 2x^3y - 4x^2y + 8xy - 16y, would the factored expression no longer be equivalent to your answer on Part B? Explain your reasoning.

Answer 1

2y(x^3 + 4x - 2x^2 - 8) ==== A
2y(x - 2)(x^2 + 4) ===== B

if 2 middle terms were switched..
2x^3y - 4x^2y + 8xy - 16y
2y(x^3 - 2x^2 + 4x - 8)
2y(x^2 + 4)(x - 2) ==== It is equivalent to answer on part B

Answer 2

Thank you so much! :)

Answer 3

Do you think you can show how you got step B please?

Answer 4

I don't really know how to explain it....it is kinda like the reverse of the FOIL method.

Answer 5

@eliassaab ..can you help with this. I do not really know how to explain to HMT how I got step B

Answer 6

It is the commutative property of addition
- 4x^2y + 8xy = + 8xy - 4x^2y
So nothing change. The two quantities are the same.

Answer 7

I think he is asking how I completely factored..not just the GCF, but the reverse FOIL stuff

Answer 8

Ok, first I'm a she. And second, I know that changing the order doesn't make a difference in the answer. I was wondering if you guys could show me the steps of how you the answer in part B.

Answer 9

* got the answer

Answer 10

Two equal expression will have the same factorization. It is a simple as that.

Answer 11

sorry bout that....she

Answer 12

It's all good.

Answer 13

Do you know the FOIL method ?

Answer 14

F ~ First term * first term
I ~ Inside term * inside term
O ~ Outside term * outside term
L ~ Last term * last term

Answer 15

ok...good..now look at this..2y(x^3 + 4x - 2x^2 - 8)

with FOIL ... 2y (x - 2)(x^2 + 4)
first ... x * x^2 = 3x^2
outside .. x * 4 = 4x
inside .. -2 * x^2 = -2x^2
last .. -2 * 4 = 8
when they are put all together, they equal 3x^2 + 4x - 2x^2 + 8....it equals.
I am not sure how to explain how to do this....I do it in my head.

Answer 16

I am sorry that I can't help more. You might want to post another question relating to how to do the reverse FOIL and somebody else can probably explain it better to you

Answer 17

Ohh, ok. I got it! No, that's ok. I just needed basic instructions, the teachers teach it all crazy and it gets confusing. Yours was much easier to understand. Thank you soo much!

Answer 18

some teachers are like that...lol.

Answer 19

Haha yea.