anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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jdoe0001
  • jdoe0001
so....have you done any factoring? have you covered factoring?
anonymous
  • anonymous
yes I have
anonymous
  • 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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jdoe0001
  • jdoe0001
ok well.. let's start backwards any ideas on say C) since is very simple \(\bf x^2-36\) ?
anonymous
  • anonymous
are the answers I put at the bottom of my question right @jdoe0001
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
  • anonymous
okay so I would explain this one by saying the square root of 36 is 6
jdoe0001
  • jdoe0001
yes, or that 36 is the square of 6 and thus it makes it a difference of squares
anonymous
  • anonymous
so that is showing work on factoring?
jdoe0001
  • jdoe0001
for C), yes
jdoe0001
  • 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
  • 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
  • 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
  • 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
  • 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
  • triciaal
|dw:1438902732501:dw||dw:1438903011604:dw|
anonymous
  • 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
  • triciaal
|dw:1438903164217:dw|
anonymous
  • anonymous
so is this 3x(x-2)+4(x-2) the final answer and not y^2(3x+4)(x-2) @triciaal
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
  • anonymous
I took notes and can I tell you what I have and see if its all of them
triciaal
  • triciaal
you can apply the steps for any factoring
anonymous
  • 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
  • anonymous
is that it and if not what would be next or changed? @triciaal
triciaal
  • triciaal
I wrote out everything above look again and go all the way to the end
anonymous
  • anonymous
okay so it y^2(3x+4)(x-2)
triciaal
  • triciaal
yes and why |dw:1438905177813:dw|
anonymous
  • 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
  • triciaal
do you understand the steps now?
anonymous
  • anonymous
yes
triciaal
  • triciaal
do it this way and I will review by the way what @jdoe0001 did is correct just not all the details
anonymous
  • anonymous
|dw:1438905441189:dw|
anonymous
  • anonymous
@triciaal
triciaal
  • triciaal
|dw:1438905837998:dw||dw:1438905995999:dw|
triciaal
  • triciaal
do you want to try this one x^2 + 7x + 12
anonymous
  • anonymous
so to factor find a,b,c then find the common one and that's it
triciaal
  • 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
  • triciaal
what is your a,b,c here
anonymous
  • anonymous
a is x^2 b is 7x and c is 12
triciaal
  • triciaal
a, b, c are just the numbers
triciaal
  • triciaal
we use a, b, c for the general equation
anonymous
  • anonymous
okay so bis 7 and c is 12 but im not sure what a is maybe 1
triciaal
  • triciaal
correct
triciaal
  • triciaal
a*c = 1* 12 = 12 next step factors of 12
anonymous
  • anonymous
1,12 2,6, 3,4
triciaal
  • 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
  • anonymous
okay so the next step would be to regroup in two sets?
triciaal
  • triciaal
we rewrite before we can group
triciaal
  • triciaal
|dw:1438907098686:dw|
anonymous
  • anonymous
ooo then would you use FOIL
triciaal
  • triciaal
|dw:1438907153246:dw|
triciaal
  • triciaal
|dw:1438907213735:dw|
anonymous
  • anonymous
I goy an answer of 15x^2+55x but I don't think that's right
anonymous
  • anonymous
okay I see it now
triciaal
  • triciaal
think of FOIL and factor as opposites FOIL to expand and factor to "put in parenthesis"
anonymous
  • 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
  • triciaal
|dw:1438907593062:dw|
triciaal
  • triciaal
|dw:1438907801534:dw|
triciaal
  • triciaal
beauty of math no one approach for the same solution
anonymous
  • 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
  • triciaal
yes
anonymous
  • 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
  • triciaal
you are welcome all the best

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