Can someone solve this math equation please?

Question

x^8 + 8x^2

Factor. This equation reads: "(x to the eigth power) plus (eight [times] (x squared)

The solution is: x^2(x^2 + 2)(x^4 - 2x + 4)

I just don't know how to get this solution. I am stumped! Thanks!

CORRECTION: The solution is:

x^2(x^2 + 2)(x^4 - 2x^2 + 4)

Answer 1

Alright, let me break this down for you

Question: Factorize x^8 + 8x^2

Answer: x^2(x^2 + 2)(x^4 - 2x + 4)

Step 1:
Looking at x^8 + 8x^2, we see that x^2 is common to both elements of the equation. So factorizing this out of the equation would be putting us on the right track to the solution.
so..
x^8 + 8x^2 = x^2(x^6 + 8)

Step 2:
We now have x^2(x^6 + 8). Our task now is to expand the bits inside the brackets. To do so we need to see that by writing 8 as a power of 2 and x^6 as a power of x^2, we can use a simple mathematical formula that'll lead us straight to the solution.
so
let 8= 2^3 and x^6= (x^2)^3

x^2[ (x^2)^3 + 2^3 ]

and using m^3 + n^3= (m + n)(m^2 - mn + n^2)

i.e m= x^2 and n= 2

we get the solution!
-------------------------------------
x^2[(x^2 + 2)(x^4 - 2x^2 + 4)]
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Answer 2

First, that is not an equation. What you have to do is to decompose that expression into some factors.

You have x^8 + 8 x^2 = x^2(x^6+8) = x^2((x^2)^3 + 2^3).

You should know that a^3 + b^3 = (a+b)(a^2-ab+b^2), so your expression becomes:

x^8 + 8x^2 = x^2(x^2+2)(X^4 - 2x + 4).

I guess you just didn't know the formula.

Answer 3

x^8 + 8x^2 = x^2 (x^6 + 8) = x^2 ( (x^2)^3 + 2^3)

Sum of two cubes factors in to:

(x^2 + 2)(x^4 -2x^2 + 4)

Putting it all together

x^2 (x^2 + 2)(x^4 - 2x^2 + 4)

Notice that your answer was almost right except you forgot that
-2x should be -2x^2

Answer 4

X^2(x^6+8)

X^2((X^2)^3+2^3) this in form (u^3+v^3)

X^2(x^2+2)(x^4-2x+4)

Answer 5

x^2((x^6) +8))

(x^2)^3+2^3=(x^2 + 2)(x^4 - 2x^2 + 4)
formula:
a^3+b^3=(a+b)(a^2-ab+b^2)

Answer 6

the soloution is very simple ..,first take the common factor out in ur equation is gonna be x^2
so it will look something llike this ...
X^8+8x^2=x^2(X^6+8)
divide X^6+8 using long division by x^2+2
u will get ur answer

Answer 7

simple really :

take the x^2 out
then you get it a format a^3+b^3
x^2[(x^2)^3 + 2^3]

btw, a^3 + b^3 = (a+b)(a^2 +b^2 -ab)

just ust that formula and you'll get you answer