Question

3x3y + 12xy - 9x2y - 36y

Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work. (3 points)

Part B: Rewrite the expression completely factored. Show the steps of your work. (4 points)

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. (3 points)

Answer 1

i dunno sry...

Answer 2

3x^3y + 12xy - 9x^2y - 36y

Answer 3

@jdoe0001 @dan815 @easyas123 can you guys help llovereading plz

Answer 4

any ideas on the GCF?

Answer 5

nope. im done for the day. my mind is literally tired. cant even think straight

Answer 6

hhhehe... I meant @ilovehim121511 =)

Answer 7

i would but i dont have time... sorry! DX

Answer 8

ohh shoot.. wrong nick =)

Answer 9

heheh ohh man I meant @Ilovereading

Answer 10

so anyhow... \(\bf 3x^3y + 12xy - 9x^2y - 36y\implies {\color{brown}{ 3}}x^3{\color{brown}{ y}} + {\color{brown}{ 3}}\cdot 4x{\color{brown}{ y}} - {\color{brown}{ 3}}\cdot 3x^2{\color{brown}{ y}} - {\color{brown}{ 3}}\cdot 12{\color{brown}{ y}}\)

what do you think @Ilovereading could be the GCF?

Answer 11

ok,

Answer 12

\(\bf 3x^3y + 12xy - 9x^2y - 36y\implies 3y(x^2+4x-3x^2-4y)\) right?

Answer 13

so it would be 3y(x^3 + 4x -3x^2 -12)?

Answer 14

@jdoe0001

Answer 15

hm actually shoot, got a typo
should be \(\large \bf 3x^3y + 12xy - 9x^2y - 36y\implies 3y(x^2+4x-3x^2-12y)\)

Answer 16

notice after plucking out the "3y" from the terms, all that's left is \(\large \bf {\color{brown}{ 3}}x^3{\color{brown}{ y}} + {\color{brown}{ 3}}\cdot 4x{\color{brown}{ y}} - {\color{brown}{ 3}}\cdot 3x^2{\color{brown}{ y}} - {\color{brown}{ 3}}\cdot 12{\color{brown}{ y}}\) is what's black

Answer 17

oh ok

Answer 18

yes

Answer 19

so it would be (x^2+4)(x-3)?

Answer 20

so to factor it... then well close

Answer 21

hmmm shoot.. just notice yet another typoe... lemme correct that first
\(\large \bf 3x^3y + 12xy - 9x^2y - 36y\implies 3y(x^2+4x-3x^2-12)\)

Answer 22

then it would be 3y(x(x^2+4) - 3x^2 - 12
3y(x(x^2+4) - 3(x^2 + 4))?

Answer 23

hmm one sec shoot lemem correct even that ohh may should be a 3 exponent there \(\large \bf 3x^3y + 12xy - 9x^2y - 36y\implies 3y(x^3+4x-3x^2-12)\)

Answer 24

ok

Answer 25

\(\bf 3x^3y + 12xy - 9x^2y - 36y\implies
\begin{array}{llll}
3y[&x^3+4x&-3x^2-12]\\
&x(x^2+4)&-3(x^2+4)\\
&(x-3)&(x^2+4)
\end{array}\)

Answer 26

or \(\large \bf 3y[(x-3)(x^2+4)]\)

Answer 27

oh okay so i was right. ok thanks! :) what about part C? i =m having trouble with that

Answer 28

part C if we swap the middle terms
ok

so let's see that \(\bf 3x^3y {\color{brown}{ - 9x^2y+ 12xy}} - 36y\implies
\begin{array}{llll}
3y[&x^3-3x^2&+4x-12]\\
&x^2(x-3)&+4(x-3)\\
&(x^2+4)& (x-3)
\end{array}\\
3y[(x^2+4)(x-3)]\)

Answer 29

notice the two factored forms \(\large \bf { B\to 3y[(x-3){\color{brown}{ (x^2+4)}}]\\
C\to 3y[{\color{brown}{ (x^2+4)}}(x-3)] }\)

Answer 30

yes

Answer 31

they're pretty much equivalent, since for factors, it doesn't quite matter the order
2* 4 = 8 or 4* 2 = 8 anyway

Answer 32

would i write that on my paper? the part with the question mark