Please help! Show me how to factor these binomials!
m^4256 and z^3+125, thank you! Descriptions are appreciated :)
 anonymous
Please help! Show me how to factor these binomials!
m^4256 and z^3+125, thank you! Descriptions are appreciated :)
 Stacey Warren  Expert brainly.com
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 katieb
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 anonymous
m^4256
this is a perfect square
 anonymous
because 2*2=4, right?
 anonymous
the 1 you want to concentrate on is 256
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 anonymous
ok
 asnaseer
try and get it into the form \(a^2b^2\)
Use the hints that mth3v4 has given you.
 anonymous
cool pic asna :D
 asnaseer
thx :) I'm actually an alien from another planet :D
 anonymous
:)
 asnaseer
Starshine7  can you express 256 as (something)^2 ?
 anonymous
16x16?
 anonymous
:)
 asnaseer
good, now can you express \(m^4\) as (something)^2 ?
 anonymous
so can you put that in in a factored form
 anonymous
m*m*m*m?
 asnaseer
Yes, so \(m^4=(m^2)^2\)
Now use those two to get the expression into the form \(a^2b^2\) so that you can then factor it like this:\[a^2b^2=(a+b)(ab)\]
 anonymous
why is it written like (m+number)(trinomial)? final answer i mean. If it helps, I factor by grouping if i can incorporate that somehow
 asnaseer
just do this one step at a time and al will be revealed :)
 anonymous
ok
 anonymous
lol oops
 anonymous
nothing happened
 asnaseer
:)
 asnaseer
Starshine7  are you stuck?
 anonymous
Sadly yes :(
 anonymous
look at the first answer you gave me
 anonymous
how did you come up with that ?
 asnaseer
ok, we saw above that:\[256=16^2\]\[m^4=(m^2)^2\]so now we can rewrite your original equation as:\[m^4256=(m^2)^216^2\]now mak use of:\[a^2b^2=(a+b)(ab)\]to simplify this further.
 anonymous
after that if can be factored again
as an option
as you can see
 anonymous
(m^2)^2 confuses me
 anonymous
(i think i am confusing starshine)
 asnaseer
ok, lets use a substitution to make it clearer...
 asnaseer
let \(n=m^2\), then we have:\[m^4256=(m^2)^216^2=n^216^2\]
 anonymous
why n? o.O
 asnaseer
we could use any other symbol  it doesn't really matter
 asnaseer
the point is it is now in the form \(a^2b^2\)
 asnaseer
so you should now be able to factorise it.
 anonymous
okies
properties of exponents state
when you multiply exponent and exponent
you add the exponent values together
(a^x)(a^b)=a^x+b
 anonymous
exponent properties/laws of exponents
whatever
 asnaseer
Starshine7  are you familiar with the exponent laws mth3v4 has shown?
i.e.:\[(x^a)^b=x^{ab}\]
 anonymous
If it helps I dont understand when a and b are examples, I was taught using only the numbers, so thats why im really confused :(
 anonymous
those are just any number
 anonymous
I know >_> Im weird like that
 asnaseer
so you are comfortable with something like this:\[18^216^2=(18+16)(1816)\]but when replaced with symbols like this:\[a^2b^2=(a+b)(ab)\]you get lost?
 anonymous
Yes, exactly :)
 asnaseer
ok  the 'a' and 'b' are just placeholders for any number
 anonymous
I just have attention issues so the numbers help me understand it better, i drift easily.
 asnaseer
what this says is that the formula:\[a^2b^2=(a+b)(ab)\]is true for ANY value of 'a' and 'b'
 asnaseer
so in your example above, we ended up with:\[m^4256=(m^2)^216^2=n^216^2\]which means we can think of it as a=n and b=16 to get:\[n^216^2=(n+16)(n16)\]we can then substitute back \(n=m^2\) to get:\[m^4256=(n+16)(n16)=(m^2+16)(m^216)\]
 asnaseer
do you understand those steps?
 anonymous
I think so
 anonymous
(a ^x ) ( a ^b )= a^x+b
^ ^ ^ ^ ^ ^ ^
    /  
 L ________ L _ ___L_ _ L _ exponent number both x and b can be any number
  
your number ______ 
 anonymous
does my funny drawing help XD
 asnaseer
ok, so now you should notice that we have \((m^216)\) as one of the factors. since \(16=4^2\), we can write this as:\[(m^216)=(m^24^2)=(m+4)(m4)\]using the same formula.
we therefore end up with:\[m^4256=(m^2+16)(m+4)(m4)\]
 anonymous
So you just keep factoring to the lowest numbers that are perfect squares?
 asnaseer
yes
 asnaseer
mth3v4  you have a lot of patience to draw all that :)
 anonymous
lol
 anonymous
:)
 anonymous
it still comes out a bit messy
 anonymous
(a^x) (a^y) = a ^ x+y
lemme try this
you have this thing here right starshine?
 asnaseer
Starshine7  for your second expression, you need to use the following factorisation:\[a^3+b^3=(a+b)(a^2ab+b^2)\]so you need to get your expression:\[z^3+125\]into the form \(a^3+b^3\)
 anonymous
okies finish what you have first
 anonymous
I guess
 asnaseer
I have to go now guys  Starshine I am sure mth3v4 will help you with the rest. Good luck all...
 anonymous
Aww..well bye Asna :) thanks anyways
 anonymous
kk bb
 asnaseer
yw
 anonymous
z^3+125 is your next 1
 anonymous
Yes
 anonymous
it is not going to be squared
but cubed
 anonymous
have you heard of
diff of cubes
or sum of cubes
formulas
 anonymous
no
 anonymous
so what ansa wrote there before leaving was
formula for
diff of cubes
 anonymous
because you just see
just a 2 termed expression here
 anonymous
so how would you make
x^3
and change it to
x^2
 anonymous
better yet lemme ask the question another way
how do you get
x^3
from
x^2
 anonymous
I'm not sure. I think they only have 2 exs in common
 anonymous
okies
lets try this
( a^x ) ( a^y ) = a ^ x +y
the variable
"a"
can be any number 1, 2, 3, whatever, happy face , i dont care what you want it to be
ok so far
 anonymous
this just goes fot the variable
"a"
we good?
 anonymous
yes
 anonymous
then next
this for the variables
"x, y"
these give a numeric value (these have to be a number)
giving a value
( a^x ) ( a^y) = a ^ x + y
 anonymous
so in the end
the numeric value of your
"a" exponent value "x"
"a" exponent value "y"
they add up
result for the a ^ x + y
is this more understandable?
 anonymous
Yes
 anonymous
so can we try that again
how to get
x^3
from
x^2
 anonymous
(x)(x+x)?
 anonymous
i just want it from x^2
 anonymous
I'm sorry I have no idea what to do :(
 anonymous
since it is already squared right
(x^2)(x)=x
how many more "x"
do we need for x ^3
 anonymous
x^2
 anonymous
you have x^2 already
 anonymous
but x^3 is made up of x^3 theres not anything left to do
 anonymous
remember
(x^2)(x)=x?
^

value of exponent you are adding to the result
 anonymous
lol
if there is nothing then say nothing
 anonymous
be more sure of you self
now just give the reason
 anonymous
nm that its probably more difficult to explain
 anonymous
but do you understand how it works
 anonymous
thats all i want to know
 anonymous
How about we start over with a new problem, m^3+216n^3 Show me in steps how to solve this and ill try another on my own, this might work
 anonymous
okeedokee
 anonymous
lol
this is differnt now because it has 2 variables in it
 anonymous
okie now
we can use something called
difference of squares
a^3+b^3= (a+b) (a^2ab+b^2)
 anonymous
ok
 anonymous
first of all you must clearly understand
the laws of exponents
(or at least the, 1 i showed you, you will have to use it for these problems )
 anonymous
we can go over it again
i dont mind
 anonymous
sure :)
 anonymous
okie
i will put a sample problem
(x^3) (x^3 )=x ^6
the exponents values of "x " add up together
(d ^100) ( d ^ 90) = d ^ 190
exponents values of "d" add up together
 anonymous
does this make sense :)
 anonymous
yes
 anonymous
"for now" <note i can go over with the rest of the laws but i hhave limited time
this is what you will need
difference of squares
a^3+b^3= (a+b) (a^2ab+b^2
 anonymous
ok
 anonymous
m^3+216n^3
know what you are working with
m^3 + 216n^3
^ ^
first term 
second term
 anonymous
a^3+b^3= ( a+b ) (a^2 ab+ b^2)
^ ^
you only have "items" that you are going to be multiplying using
FOIL with
 anonymous
a^3+b^3= (a+b) (a^2ab+b^2)
 ^ ^
 this part wants the numbers squared to
 be multiplied with
L
 anonymous
how do we get a squared variable to be cubed? :)
 anonymous
^3?
 anonymous
m^2
to
m^3
 anonymous
add another m?
 anonymous
type how you would do that plz :)
 anonymous
its correct but how would it look
 anonymous
mathematically
 anonymous
give you a hint
its not x+x
 anonymous
that is called adding like terms
 anonymous
it becomes 2x
 anonymous
remember this model
(a ^ x) ( a ^y ) = a ^x+y
 anonymous
x is going to be your a variable
 anonymous
the values of your exponent to the x are?
 anonymous
i gave you already x^2
you have x^2
how much you need to get to
x^3
 anonymous
(x ^ 2) ( x ^y ) = x ^2+y
what will you need to get 3
 anonymous
as the exponent result
 anonymous
x
 anonymous
correct :)
 anonymous
so the value of that 1 that you are missing is just
x
 anonymous
^^
 anonymous
it is because
x*x*x = x^3
but i think you know that
 anonymous
do you know how to simplify radicals
 anonymous
I do
 anonymous
im sorry i have chat lag :(
 anonymous
cube root of 216 is
6
but you want
6^2
and
n^2
so you can do the FOIL
 anonymous
sorries i gtg now :(
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