I will fan and medal
can you please help mw with the steps
Part A: Factor 3x^2y^2 − 2xy^2 − 8y^2. Show your work. (4 points)
Part B: Factor x^2 + 10x + 25. Show your work. (3 points)
Part C: Factor x^2 − 36. Show your work. (3 points)
these are my answers
part a: y^2=(3x+4)(x-2)
part b: (x+5)(x+5)
part c: (x+6)(x-6)

- anonymous

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- jdoe0001

so....have you done any factoring? have you covered factoring?

- anonymous

yes I have

- anonymous

I can check my answer using the FOIL method I just don't know the steps to factoring if that makes sense @jdoe0001

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## More answers

- jdoe0001

ok
well.. let's start backwards
any ideas on say C) since is very simple \(\bf x^2-36\) ?

- anonymous

are the answers I put at the bottom of my question right @jdoe0001

- jdoe0001

hmm ok
well, those are given, but anyhow
\(\bf x^2-36\qquad {\color{brown}{ 6^2=36}}\qquad thus\implies x^2-6^2
\\ \quad \\
--------------------------\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\
--------------------------------------\\
x^2-6^2\implies (x-6)(x+6)\)

- anonymous

okay so I would explain this one by saying the square root of 36 is 6

- jdoe0001

yes, or that 36 is the square of 6
and thus it makes it a difference of squares

- anonymous

so that is showing work on factoring?

- jdoe0001

for C), yes

- jdoe0001

B) is also simple
if we factor 25, we get 5, 5, 1 5*5*1 = 25
if we "multiply" then 5*5 we get the last term
if we "add" 5+5, we get the middle term
thus \(\begin{array}{cccllll}
x^2&+10&+25\\
&\uparrow &\uparrow \\
&5+5&5\cdot 5
\end{array}\implies (x+5)(x+5)\)

- anonymous

okay so if I were to explain it, it would be in order to factor x^2+10x+25 you pull out the GCF which in this case is 5 and simplify to (x+5)(x+5)

- jdoe0001

well... 5 is not the GCF, notice \(x^2\) doesn't have a 5
you'd factor out the last term, the constant one
and from a combination of two of its factors
you ought to get the middle term

- anonymous

so from the original problem of x^2+10x+25 you would factor the 10 and 25 and that's is supposed to be explaining the steps of how you get this answer?

- jdoe0001

hmm
well... you said you have already covered factoring
so...... you should recall that you need to factor out the constant
to get the values for the binomials

- triciaal

|dw:1438902732501:dw||dw:1438903011604:dw|

- anonymous

so by factoring out 25 we get 5*5 which will give us the two numbers we need but then would you take the square root of x cause you have to have two x's in the end

- triciaal

|dw:1438903164217:dw|

- anonymous

so is this 3x(x-2)+4(x-2) the final answer and not y^2(3x+4)(x-2) @triciaal

- triciaal

I had +2 instead of +4 for the factors but correctly used + 4 for a sum of -2 made the correction
|dw:1438903609253:dw|
do you understand all the steps ?

- anonymous

I took notes and can I tell you what I have and see if its all of them

- triciaal

you can apply the steps for any factoring

- anonymous

so first you take out the term y^2
then you have y^2(3x^3-2x-8)
identify a,b,c
3(-8) =-24
use -6,4
3x^2-6x+4x-8
3x(x-2)+4(x-2)

- anonymous

is that it and if not what would be next or changed? @triciaal

- triciaal

I wrote out everything above look again
and go all the way to the end

- anonymous

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

- triciaal

yes and why |dw:1438905177813:dw|

- anonymous

okay can you help me with the second one too its
Part B: Factor x^2 + 10x + 25. Show your work. (3 points

- triciaal

do you understand the steps now?

- anonymous

yes

- triciaal

do it this way and I will review
by the way what @jdoe0001 did is correct just not all the details

- anonymous

|dw:1438905441189:dw|

- anonymous

@triciaal

- triciaal

|dw:1438905837998:dw||dw:1438905995999:dw|

- triciaal

do you want to try this one
x^2 + 7x + 12

- anonymous

so to factor find a,b,c then find the common one and that's it

- triciaal

identify a, b, c
multiply a by c and list the factors
choose the combination of factors that will add up to b pay attention to the signs
rewrite the middle term using the sum of the factors
regroup and factor ( the 2 sets )
identify the common term in the 2 sets
factor out the common term from the 2 sets
what you get is the complete factorization of the original

- triciaal

what is your a,b,c here

- anonymous

a is x^2 b is 7x and c is 12

- triciaal

a, b, c are just the numbers

- triciaal

we use a, b, c for the general equation

- anonymous

okay so bis 7 and c is 12 but im not sure what a is maybe 1

- triciaal

correct

- triciaal

a*c = 1* 12 = 12
next step factors of 12

- anonymous

1,12 2,6, 3,4

- triciaal

review the instructions also the negatives
we want the combination that when added will give b in this case +7 so we use +4 and +3

- anonymous

okay so the next step would be to regroup in two sets?

- triciaal

we rewrite before we can group

- triciaal

|dw:1438907098686:dw|

- anonymous

ooo then would you use FOIL

- triciaal

|dw:1438907153246:dw|

- triciaal

|dw:1438907213735:dw|

- anonymous

I goy an answer of 15x^2+55x but I don't think that's right

- anonymous

okay I see it now

- triciaal

think of FOIL and factor as opposites
FOIL to expand and factor to "put in parenthesis"

- anonymous

okay thank you so for part c I know the other person said the steps but could you review what I have from it

- triciaal

|dw:1438907593062:dw|

- triciaal

|dw:1438907801534:dw|

- triciaal

beauty of math no one approach for the same solution

- anonymous

okay I see it now thank you so much and once we group I=the final answer will be (x+6)(x-6)

- triciaal

yes

- anonymous

omg thank you so much I wish I could give you a million medals you have been a life saver especially working with me for so long

- triciaal

you are welcome all the best

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