Match each expression to its equivalent standard form

1. x² + 2x + 2

2. x² + 4

3. x² - 4x + 8

Step-by-step explanation:

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

= ( x+1 )²- i²  [ Since ( a+b ) ( a-b ) = a² - b² ]

= x² + 1 + 2x - ( √-1 )²

= x² + 1 + 2x + 1

= x² + 2x + 2

(2) ( x+2i ) ( x - 2i )

= x² - (2i)² [ ( a+b ) ( a-b ) = a² b²

= x² - 4i²

= x² - 4 (-1) [Since i² = -1 ]

= x² + 4

(3) ( x - 2i - 2 ) (x + 2i - 2 )

= ( x-2 )² - ( 2i )² [ ( a+b ) ( a-b ) = a² - b² ]

= x² + 4 - 4x - 4 ( i )²

= x² + 4 - 4x - 4 ( -1 )²

= x² - 4x + 4 + 4

= x² - 4x + 8

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step-by-step explanation: