Question

a8+a4+1 factorization​

Answer 1

Answer:

hey mate

Here's ur answer.....

(a^4)^2 + (a^2)^2 + 1 =0

let us consider a^2 as m

m^2+m+1=0

This can't be factorize further....

I think so the question is wrong.....

it should be like-

a^8+2a^4+1=0

m^2+2m+1=0

m^2+m+m+1=0

m(m+1)+1 (m+1)=0

(m+1)(m+1)=0

m=-1,-1.....

but m=a^2

a=1,1.......

hope it helps

Fllw karna mat bhulyo and mark it as brainliest. dude

Answer 2

Answer:

a8 + a4 + 1 = (a^2 + 1 - a)(a^2 +1 + a)(a^4 + 1 -a^2)

Step-by-step explanation:

Use the method of Completing Square :

= (a^4)^2 + 1 + a^4 + 2(1)(a^4) -2(1)(a^4)

using formula of (a+b)^2 = a^2 + b^2 + 2ab

Given expression becomes :

= (a^4 + 1)^2 + a^4 - 2a^4

= (a^4 +1)^2 - a^4   =  (a^4 +1)^2 - (a^2)^2

Using formula of a^2 - b^2 = (a+b)(a-b)

= (a^4 +1 + a^2) (a^4 +1 - a^2)

again complete square of bolded term

= (a^4 +1 - a^2) (a^4 +1 + a^2)

= (a^4 +1 - a^2) ( a^2^2 + 1 + 2a^2 -2a^2 +a^2)

use formula of (a^2 + b^2 +2ab) = (a+b)^2

= (a^4 +1 - a^2) [(a^2 + 1 )^2 - 1a^2)    

Using formula of a^2 - b^2 = (a+b)(a-b)

=  (a^4 +1 - a^2) ( a^2 +1 - a ) ( a^2 +1 +a)