Question

The expression x⁴ + 4 can be factorized as

Options

• (x² + 2x + 2) (x² − 2x + 2)

• (x² + 2x + 2) (x² + 2x + 2)

• (x² − 2x − 2) (x² − 2x + 2)

• (x² + 2) (x² − 2)

Answer 1

The given expression to be factorized is  x⁴ + 4

This can be written in the form 

 x⁴ + 4 =` (x^2)^2 + (2)^2 + 2x^2 2.- 4x^2`

` = {(x^2)^2 +2.x^2 . 2+ (2)^2} - (2x)^2`

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

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