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)

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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)

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so....have you done any factoring? have you covered factoring?
yes I have
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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ok well.. let's start backwards any ideas on say C) since is very simple \(\bf x^2-36\) ?
are the answers I put at the bottom of my question right @jdoe0001
hmm ok well, those are given, but anyhow \(\bf x^2-36\qquad {\color{brown}{ 6^2=36}}\qquad thus\implies x^2-6^2 \\ \quad \\ --------------------------\\ \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\ --------------------------------------\\ x^2-6^2\implies (x-6)(x+6)\)
okay so I would explain this one by saying the square root of 36 is 6
yes, or that 36 is the square of 6 and thus it makes it a difference of squares
so that is showing work on factoring?
for C), yes
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 \(\begin{array}{cccllll} x^2&+10&+25\\ &\uparrow &\uparrow \\ &5+5&5\cdot 5 \end{array}\implies (x+5)(x+5)\)
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)
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
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?
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
|dw:1438902732501:dw||dw:1438903011604:dw|
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
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so is this 3x(x-2)+4(x-2) the final answer and not y^2(3x+4)(x-2) @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 ?
I took notes and can I tell you what I have and see if its all of them
you can apply the steps for any factoring
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)
is that it and if not what would be next or changed? @triciaal
I wrote out everything above look again and go all the way to the end
okay so it y^2(3x+4)(x-2)
yes and why |dw:1438905177813:dw|
okay can you help me with the second one too its Part B: Factor x^2 + 10x + 25. Show your work. (3 points
do you understand the steps now?
yes
do it this way and I will review by the way what @jdoe0001 did is correct just not all the details
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do you want to try this one x^2 + 7x + 12
so to factor find a,b,c then find the common one and that's it
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
what is your a,b,c here
a is x^2 b is 7x and c is 12
a, b, c are just the numbers
we use a, b, c for the general equation
okay so bis 7 and c is 12 but im not sure what a is maybe 1
correct
a*c = 1* 12 = 12 next step factors of 12
1,12 2,6, 3,4
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
okay so the next step would be to regroup in two sets?
we rewrite before we can group
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ooo then would you use FOIL
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I goy an answer of 15x^2+55x but I don't think that's right
okay I see it now
think of FOIL and factor as opposites FOIL to expand and factor to "put in parenthesis"
okay thank you so for part c I know the other person said the steps but could you review what I have from it
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beauty of math no one approach for the same solution
okay I see it now thank you so much and once we group I=the final answer will be (x+6)(x-6)
yes
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
you are welcome all the best

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