Question

prove that
${x}^{4} + 4 = (x + 1 + i)(x + 1 - i)(x - 1 + i)(x - 1 - i)$
​

Answer 1

Answer:

Step-by-step explanation:

(x+1+i)(x+1-i)=[(x+1)^2-(i^2)]=x^2+2x+1-(i^2)=x^2+2x+2

i^2=-1

(x-1+i)(x-1-i)

x-1 as one term

i as another

use (a+b)(a-b) formula

(x-1+i)(x-1-i)=x^2-2x+2

now (x^2+2x+2)(x^2-2x+2)

now x^2+2 as one term

and 2x as another

use (a+b)(a-b) formula

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

=x^4+4

Answer 2

k...now.....

there was a problem in posting this pic yesterday.....!!

hope it helps u buddy......!!