Can someone help me with this please?

An expression is shown below:

$$3x^3y + 12xy - 3x^2y - 12y$$

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 3x3y - 3x2y + 12xy - 12y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning.

Thanks for helping!

Question

Can someone help me with this please?

An expression is shown below:

$$3x^3y + 12xy - 3x^2y - 12y$$

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 3x3y - 3x2y + 12xy - 12y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning.

Thanks for helping!

anonymous · Answer

@Hero @pooja195 @Abhisar @triciaal @jigglypuff314 @SolomonZelman @Directrix @mathmale @mathstudent55 @zepdrix

anonymous · Answer

I'll be back in about 10 - 15 minutes

anonymous · Answer

Nvm I'm back. @triciaal can you help?

zela101 · Answer

What does "GCF" mean?

anonymous · Answer

@Zela101 Greatest common factor

zela101 · Answer

What is the GCF here?

zeronknight · Answer

Do you know what GCF is, or means? @Needhelpstudying

anonymous · Answer

@Zela101 It's either 3x, 3x3, or 3x3y. idk my brain turned off and I'm sick lol

zela101 · Answer

$$3x^3y + 12xy - 3x^2y - 12y$$
is x found in every term?

anonymous · Answer

No.

zela101 · Answer

Is x a GCF then?

anonymous · Answer

Nope

anonymous · Answer

the GCF is all values that they share, 3y is the common factor that they all share.

so, factoring it out we get:
3y ( x^3 + 4x - x^2 - 4 )

zela101 · Answer

So the GCF cannot have an x. Eliminate your choices for 3x, 3x^3, or 3x^3y because contains an X or Xs

anonymous · Answer

So the GCF would be 3y?

anonymous · Answer

yes

zela101 · Answer

Yes because there's a factor of 3 obviously and every term has at least 1 y.

anonymous · Answer

part B is basically u showing steps of part A

anonymous · Answer

And I already know how to factor out things. @ayeshaafzal221 Did that for me though. So that answers A.

anonymous · Answer

yes

anonymous · Answer

@ayeshaafzal221 Is it completely factored with the answer you gave me?

zela101 · Answer

@ayeshaafzal221 you should not factor and give out answers like that without walking the users to the answer.

anonymous · Answer

i just factor out y thats not the answer @Zela101

anonymous · Answer

Technically it is lol

zela101 · Answer

The question has more than one part

anonymous · Answer

But it doesn't matter, I know how to factor out as well.

anonymous · Answer

3y* the person has to simplify themselves

zela101 · Answer

that means it has more than one answer

zela101 · Answer

Can you shows us how you factored the expression completely from answer A?

zela101 · Answer

For part b

anonymous · Answer

ok for part C whats ur approach

anonymous · Answer

Sorry guys, I switched the tab

anonymous · Answer

Alright, I'm really sick, so sorry if I'm a bit slow. @ayeshaafzal221 When you factored out the GCF, was that equation completely factored? Like is part B just asking how you factored out the GCF, or is there more factoring after the GCF?

anonymous · Answer

@ayeshaafzal221 You there?

anonymous · Answer

yes i am asking u what approach will u take for part c

anonymous · Answer

do u think switching the terms will effect the outcome?

anonymous · Answer

When did we do part B?

anonymous · Answer

ugggh headache

anonymous · Answer

oh i thought u got part B

anonymous · Answer

No. When you factored out the GCF, was the equation fully factored? Like, am I just supposed to explain how to factor out the GCF for Part B, or am I supposed to factor further?

anonymous · Answer

for part B, start with part A
3y ( x^3 + 4x - x^2 - 4 ) 
try to factor the stuff inside parenthesis

anonymous · Answer

and show each  steps

anonymous · Answer

factor first two terms,
and last terms separately

anonymous · Answer

Alright

anonymous · Answer

3y((x^3 + 4x) - (x^2 - 4))

anonymous · Answer

$$3y(x(x^2+4)-(x^2-4))$$

anonymous · Answer

now can you see clearly what ur next step is?

anonymous · Answer

I know what you did, you got divided the first binomial by its GCF

anonymous · Answer

What would the gcf between x^2 and 4 be?

anonymous · Answer

u dont need to worry about GCF in this

anonymous · Answer

But then wut do I do next?

anonymous · Answer

$$3y((x^2+4)(x-1))$$

anonymous · Answer

thats ur answer

anonymous · Answer

wait, why did ur 4 turn into a 1, and where did the x^2 go?

anonymous · Answer

dont u know how to factor ?

anonymous · Answer

see above u got this right 3y((x^3 + 4x) - (x^2 - 4))

anonymous · Answer

$$(x^3+4x)$$

anonymous · Answer

whats a common factor in this ?

anonymous · Answer

x

anonymous · Answer

so it become $$3y(x(x^2+4)-(x^2-4))$$

anonymous · Answer

right

anonymous · Answer

now if u see closely you have two terms $$(x^2+4) and (x^2-4)$$

anonymous · Answer

Oh yeah, I see that

anonymous · Answer

and u have negative  in middle

anonymous · Answer

yea

anonymous · Answer

$$3y((x^2+4)(x-1))$$

anonymous · Answer

thats ur part B

anonymous · Answer

wait, can you just explain how you got the - 1 though. Was it something to do with the first term?

anonymous · Answer

if u e|dw:1451011031741:dw|