Question

Algebra 1 help please! I'll give a medal to anyone who helps me. :)
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Question:
An expression is shown below:

3x3y + 12xy - 9x2y - 36y

Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work.

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 - 9x2y + 12xy - 36y, would the factored expression no longer be equivalent to your answer in part B? Explain your reasoning.

Answer 1

\(\large 3x^3y + 12xy - 9x^2y - 36y\)

GCF of numbers = 3
GCF of y terms = y

pull them out, what do u get ?

Answer 2

\(\large 3x^3y + 12xy - 9x^2y - 36y\)


after factoring the 3 :
\(\large 3(x^3y + 4xy - 3x^2y - 12y)\)

after factoring the y :
\(\large 3y(x^3 + 4x - 3x^2 - 12)\)

Answer 3

^^ thats ur part A

see if that makes sense...

Answer 4

I'm confused about factoring y? how did you get that?
Everything else makes sense. :)

Answer 5

good question :)

Answer 6

look at the original given expression

Answer 7

It has 4 terms,
and each term has a "y" in it right ?

Answer 8

Here is the given expression :

\(\large 3x^3\color{red}{y} + 12x\color{red}{y} - 9x^2\color{red}{y} - 36\color{red}{y} \)

Answer 9

I have just pulled that "y" out as it is common in every term..

Answer 10

ohhh now it makes sense.

Answer 11

good :) see if u can do the part B now

Answer 12

for part B,
u need to take the Part A answer and start from there..

Answer 13

okay :)

Answer 14

part B :

\(\large 3y(x^3 + 4x - 3x^2 - 12) \)

try to factor the stuff inside parenthesis

Answer 15

factor first two terms,
and last terms separately

Answer 16

whats the GCF of first two terms ?

\(\large 3y(\color{red}{x^3 + 4x} - 3x^2 - 12) \)

Answer 17

they both have a "x" in them right ?

Answer 18

Yeah, do I have to take them out?

Answer 19

yup :)

\(\large 3y(\color{red}{x^3 + 4x} - 3x^2 - 12) \)

Factoring out GCF from first two terms gives :

\(\large 3y\left(\color{red}{x(x^2 + 4)} - 3x^2 - 12\right) \)

Answer 20

Similarly, factor the GCF from last terms, you wud get :

\(\large 3y(\color{red}{x^3 + 4x} - 3x^2 - 12) \)

Factoring out GCF from first two terms gives :
\(\large 3y\left(\color{red}{x(x^2 + 4)} - 3x^2 - 12\right) \)

Factoring the GCF from last two terms gives :
\(\large 3y\left(\color{red}{x(x^2 + 4)} - 3(x^2 + 4)\right) \)

Answer 21

fine, so far eh ?

Answer 22

Yes. :) So now I would have to factor which expression?

Answer 23

zoom out a bit and stare at the expression again

Answer 24

do u see (x^2+4) common inside the parenthesis ?

Answer 25

\(\large 3y(\color{red}{x^3 + 4x} - 3x^2 - 12) \)

Factoring out GCF from first two terms gives :
\(\large 3y\left(\color{red}{x(x^2 + 4)} - 3x^2 - 12\right) \)

Factoring the GCF from last two terms gives :
\(\large 3y\left(\color{red}{x(x^2 + 4)} - 3(x^2 + 4)\right) \)

factoring out the (x^2+4) from the terms inside parenthesis gives :
\(\large 3y(x^2 + 4)(x-3) \)

Answer 26

we're done with part B !

Answer 27

let me knw if smthng doesnt make sense..

Answer 28

Yay! Thanks so much for your help. :)

Answer 29

np :) what do u think about part C ?

Answer 30

I think I can do it. :) aha

Answer 31

Very good :)