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NationalTutoringObservatory
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MathEd-PII

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8
student
something like (x-1)(x-5)
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volunteer
Yes good job!
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student
or 2x-5)(5x+2)
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student
but these ones require a bit more steps
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volunteer
So that's what we'll be doing in this problem
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volunteer
Okay in this question, you notice that there is a common term amongst both expressions. Can you pinpoint what it is
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student
5^2+k
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student
like that?
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volunteer
Yes precisely
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student
then how do we factor it then?
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volunteer
And now you're left with h^2 - k^2 = (h-k)(h+k)
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student
those two only?
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volunteer
Also include h^2 - k^2 at the beginning of the factor
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student
there
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volunteer
You did it somewhat correctly, but I'll show you
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student
ok
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volunteer
In order to fully factor this you would need to know the difference of squares
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student
oh alr
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student
what if it was a cube
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volunteer
It would be the same process, but with cubes instead. For example h^3 - K^3 = (h-k)(h^2 + hk + k^2), which is the fully factor form if it was cube
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volunteer
But in this scenario we're working with squares, so the fully factor form will be substituting the h^2 in to a factor with k
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student
ok bc I barely get cubes
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volunteer
so (h^2 + k)(h-k)(h+k)
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student
problem 2
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volunteer
So what are you confused about in this question?
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student
what do we do with the x
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volunteer
Okay we will use x later when we recognize the differences of squares
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volunteer
So first what do you notice in this expression
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student
we have a quadratic equation
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student
the factors for that is ((u-1)^2
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volunteer
Great job Alex!
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[ { "pii_type": "PERSON", "surrogate": "Alex", "start": 10, "end": 14 } ]
volunteer
So we notice that x - 2u + 1 is a perfect square, resulting in ((u-1)^2
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volunteer
So what have right now is (u - 1)^2 - v^2
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volunteer
So what do you notice now in this expression?
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student
we have a perfect square and another term
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volunteer
That's true, but consider on what that truly means
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volunteer
This perfect square and another term tells us that there's a difference of squares
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student
a difference of squares?
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volunteer
Yes, meaning (a^2 - b^2) = (a-b)(a+b)
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volunteer
And in this scenario, what do you think a and b is?
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student
a is u-1 and b is v
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volunteer
Correct!
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volunteer
So all you have to do is fully factor it from this (u-1)^2 - v^2
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student
like that?
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volunteer
Great job! That is perfect work
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student
nice
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student
problem 3
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volunteer
How do you feel so far on this topic?
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student
factoring eh
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student
I get some of it
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student
but the bigger equations just mess me up
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volunteer
Oh okay with extra practice, I can guarantee that you'll do just fine on this upcoming test/quiz
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student
we also have two other topics to go over as well but i'm more thorough with those
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volunteer
So in this problem, what do you see in common in these expressions
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student
trying to factor it after the first step
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student
like I typically dont know what variables to factor espiecially if its a cube
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volunteer
Don't worry we'll get to that problem soon, but let's focus on this one for now
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volunteer
So in this expression, what common factor do you see
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student
y+1
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volunteer
Yes, you're on the right track
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volunteer
Yes good job Alex!
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[ { "pii_type": "PERSON", "surrogate": "Alex", "start": 13, "end": 17 } ]
student
is that correct?
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volunteer
Yes you did it correctly, but be mindful of the operation that you used for y-1
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student
y-1?
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volunteer
Good job! Yes (y-1) should be (y+1)
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student
wait im so confused
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volunteer
It's because you put (y-1) at first
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student
ohh
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student
would we combine terms?
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volunteer
I just wanted to guide you to fix that minor mistake
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student
like y+3 and y+2
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volunteer
Nope, this will be your fully factored form/expression
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student
oh
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student
I got it right
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student
thats something
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student
ill try 4
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student
and see what I get
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volunteer
After you finish, I'll guide you on what you did right or wrong
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volunteer
Also I'm very sorry that this may be my last question that I can help and support you on
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student
its fine
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volunteer
Sorry for my inconveniences
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student
is that it?
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volunteer
Not quite, but you got the first part down efficiently. Do you remember the cubes formula?
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student
A^3-B^3= A+B and A^2-B^2
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volunteer
The cubes formula: x^3 + y^3 = (x+y)(x^2 -xy + y^2)
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volunteer
a = x and b = y
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student
wait
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student
do we use the coefficient?
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volunteer
Yes
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volunteer
a = 3a and b = 4c
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volunteer
Good job, you're learning very quick
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volunteer
What did you put for c? And also, be careful of "3a^2", you'll need to square it
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student
4c^2
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volunteer
You would need to multiply is by 4c which will give you 16c^2
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student
huh
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student
why
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student
oh
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student
we have to square the bases?
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volunteer
Yes precisely
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volunteer
Since it's in factor form, you'll have to multiply each one
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