anonymous
  • anonymous
Please help! Show me how to factor these binomials! m^4-256 and z^3+125, thank you! Descriptions are appreciated :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
m^4-256 this is a perfect square
anonymous
  • anonymous
because 2*2=4, right?
anonymous
  • anonymous
the 1 you want to concentrate on is 256

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anonymous
  • anonymous
ok
asnaseer
  • asnaseer
try and get it into the form \(a^2-b^2\) Use the hints that mth3v4 has given you.
anonymous
  • anonymous
cool pic asna :D
asnaseer
  • asnaseer
thx :) I'm actually an alien from another planet :D
anonymous
  • anonymous
:)
asnaseer
  • asnaseer
Starshine7 - can you express 256 as (something)^2 ?
anonymous
  • anonymous
16x16?
anonymous
  • anonymous
:)
asnaseer
  • asnaseer
good, now can you express \(m^4\) as (something)^2 ?
anonymous
  • anonymous
so can you put that in in a factored form
anonymous
  • anonymous
m*m*m*m?
asnaseer
  • asnaseer
Yes, so \(m^4=(m^2)^2\) Now use those two to get the expression into the form \(a^2-b^2\) so that you can then factor it like this:\[a^2-b^2=(a+b)(a-b)\]
anonymous
  • 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
  • asnaseer
just do this one step at a time and al will be revealed :)
anonymous
  • anonymous
ok
anonymous
  • anonymous
lol oops
anonymous
  • anonymous
nothing happened
asnaseer
  • asnaseer
:)
asnaseer
  • asnaseer
Starshine7 - are you stuck?
anonymous
  • anonymous
Sadly yes :(
anonymous
  • anonymous
look at the first answer you gave me
anonymous
  • anonymous
how did you come up with that ?
asnaseer
  • asnaseer
ok, we saw above that:\[256=16^2\]\[m^4=(m^2)^2\]so now we can rewrite your original equation as:\[m^4-256=(m^2)^2-16^2\]now mak use of:\[a^2-b^2=(a+b)(a-b)\]to simplify this further.
anonymous
  • anonymous
after that if can be factored again as an option as you can see
anonymous
  • anonymous
(m^2)^2 confuses me
anonymous
  • anonymous
(i think i am confusing starshine)
asnaseer
  • asnaseer
ok, lets use a substitution to make it clearer...
asnaseer
  • asnaseer
let \(n=m^2\), then we have:\[m^4-256=(m^2)^2-16^2=n^2-16^2\]
anonymous
  • anonymous
why n? o.O
asnaseer
  • asnaseer
we could use any other symbol - it doesn't really matter
asnaseer
  • asnaseer
the point is it is now in the form \(a^2-b^2\)
asnaseer
  • asnaseer
so you should now be able to factorise it.
anonymous
  • 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
  • anonymous
exponent properties/laws of exponents whatever
asnaseer
  • asnaseer
Starshine7 - are you familiar with the exponent laws mth3v4 has shown? i.e.:\[(x^a)^b=x^{ab}\]
anonymous
  • 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
  • anonymous
those are just any number
anonymous
  • anonymous
I know >_> Im weird like that
asnaseer
  • asnaseer
so you are comfortable with something like this:\[18^2-16^2=(18+16)(18-16)\]but when replaced with symbols like this:\[a^2-b^2=(a+b)(a-b)\]you get lost?
anonymous
  • anonymous
Yes, exactly :)
asnaseer
  • asnaseer
ok - the 'a' and 'b' are just placeholders for any number
anonymous
  • anonymous
I just have attention issues so the numbers help me understand it better, i drift easily.
asnaseer
  • asnaseer
what this says is that the formula:\[a^2-b^2=(a+b)(a-b)\]is true for ANY value of 'a' and 'b'
asnaseer
  • asnaseer
so in your example above, we ended up with:\[m^4-256=(m^2)^2-16^2=n^2-16^2\]which means we can think of it as a=n and b=16 to get:\[n^2-16^2=(n+16)(n-16)\]we can then substitute back \(n=m^2\) to get:\[m^4-256=(n+16)(n-16)=(m^2+16)(m^2-16)\]
asnaseer
  • asnaseer
do you understand those steps?
anonymous
  • anonymous
I think so
anonymous
  • 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
  • anonymous
does my funny drawing help XD
asnaseer
  • asnaseer
ok, so now you should notice that we have \((m^2-16)\) as one of the factors. since \(16=4^2\), we can write this as:\[(m^2-16)=(m^2-4^2)=(m+4)(m-4)\]using the same formula. we therefore end up with:\[m^4-256=(m^2+16)(m+4)(m-4)\]
anonymous
  • anonymous
So you just keep factoring to the lowest numbers that are perfect squares?
asnaseer
  • asnaseer
yes
asnaseer
  • asnaseer
mth3v4 - you have a lot of patience to draw all that :)
anonymous
  • anonymous
lol
anonymous
  • anonymous
:)
anonymous
  • anonymous
it still comes out a bit messy
anonymous
  • anonymous
(a^x) (a^y) = a ^ x+y lemme try this you have this thing here right starshine?
asnaseer
  • asnaseer
Starshine7 - for your second expression, you need to use the following factorisation:\[a^3+b^3=(a+b)(a^2-ab+b^2)\]so you need to get your expression:\[z^3+125\]into the form \(a^3+b^3\)
anonymous
  • anonymous
okies finish what you have first
anonymous
  • anonymous
I guess
asnaseer
  • asnaseer
I have to go now guys - Starshine I am sure mth3v4 will help you with the rest. Good luck all...
anonymous
  • anonymous
Aww..well bye Asna :) thanks anyways
anonymous
  • anonymous
kk bb
asnaseer
  • asnaseer
yw
anonymous
  • anonymous
z^3+125 is your next 1
anonymous
  • anonymous
Yes
anonymous
  • anonymous
it is not going to be squared but cubed
anonymous
  • anonymous
have you heard of diff of cubes or sum of cubes formulas
anonymous
  • anonymous
no
anonymous
  • anonymous
so what ansa wrote there before leaving was formula for diff of cubes
anonymous
  • anonymous
because you just see just a 2 termed expression here
anonymous
  • anonymous
so how would you make x^3 and change it to x^2
anonymous
  • anonymous
better yet lemme ask the question another way how do you get x^3 from x^2
anonymous
  • anonymous
I'm not sure. I think they only have 2 exs in common
anonymous
  • 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
  • anonymous
this just goes fot the variable "a" we good?
anonymous
  • anonymous
yes
anonymous
  • 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
  • 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
  • anonymous
Yes
anonymous
  • anonymous
so can we try that again how to get x^3 from x^2
anonymous
  • anonymous
(x)(x+x)?
anonymous
  • anonymous
i just want it from x^2
anonymous
  • anonymous
I'm sorry I have no idea what to do :(
anonymous
  • anonymous
since it is already squared right (x^2)(x)=x how many more "x" do we need for x ^3
anonymous
  • anonymous
x^2
anonymous
  • anonymous
you have x^2 already
anonymous
  • anonymous
but x^3 is made up of x^3 theres not anything left to do
anonymous
  • anonymous
remember (x^2)(x)=x? ^ | value of exponent you are adding to the result
anonymous
  • anonymous
lol if there is nothing then say nothing
anonymous
  • anonymous
be more sure of you self now just give the reason
anonymous
  • anonymous
nm that its probably more difficult to explain
anonymous
  • anonymous
but do you understand how it works
anonymous
  • anonymous
thats all i want to know
anonymous
  • 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
  • anonymous
okeedokee
anonymous
  • anonymous
lol this is differnt now because it has 2 variables in it
anonymous
  • anonymous
okie now we can use something called difference of squares a^3+b^3= (a+b) (a^2-ab+b^2)
anonymous
  • anonymous
ok
anonymous
  • 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
  • anonymous
we can go over it again i dont mind
anonymous
  • anonymous
sure :)
anonymous
  • 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
  • anonymous
does this make sense :)
anonymous
  • anonymous
yes
anonymous
  • 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^2-ab+b^2
anonymous
  • anonymous
ok
anonymous
  • anonymous
m^3+216n^3 know what you are working with m^3 + 216n^3 ^ ^ first term | second term
anonymous
  • 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
  • anonymous
a^3+b^3= (a+b) (a^2-ab+b^2) | ^ ^ | this part wants the numbers squared to | be multiplied with L--------------------|
anonymous
  • anonymous
how do we get a squared variable to be cubed? :)
anonymous
  • anonymous
^3?
anonymous
  • anonymous
m^2 to m^3
anonymous
  • anonymous
add another m?
anonymous
  • anonymous
type how you would do that plz :)
anonymous
  • anonymous
its correct but how would it look
anonymous
  • anonymous
mathematically
anonymous
  • anonymous
give you a hint its not x+x
anonymous
  • anonymous
that is called adding like terms
anonymous
  • anonymous
it becomes 2x
anonymous
  • anonymous
remember this model (a ^ x) ( a ^y ) = a ^x+y
anonymous
  • anonymous
x is going to be your a variable
anonymous
  • anonymous
the values of your exponent to the x are?
anonymous
  • anonymous
i gave you already x^2 you have x^2 how much you need to get to x^3
anonymous
  • anonymous
(x ^ 2) ( x ^y ) = x ^2+y what will you need to get 3
anonymous
  • anonymous
as the exponent result
anonymous
  • anonymous
x
anonymous
  • anonymous
correct :)
anonymous
  • anonymous
so the value of that 1 that you are missing is just x
anonymous
  • anonymous
^^
anonymous
  • anonymous
it is because x*x*x = x^3 but i think you know that
anonymous
  • anonymous
do you know how to simplify radicals
anonymous
  • anonymous
I do
anonymous
  • anonymous
im sorry i have chat lag :(
anonymous
  • anonymous
cube root of 216 is 6 but you want 6^2 and n^2 so you can do the FOIL
anonymous
  • anonymous
sorries i gtg now :(

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