If Q(x)=x^2-5, find [Q(x)]^2

Question

If Q(x)=x^2-5, Find [Q(x)]^2

Answer 1

rewrie it as you can see the form

 

(x^2-5)^2

 

now write them twice 

(x^2-5) (x^2-5)

FOIL

x^4 -5x^2 -5x^2 +25

combine like terms

x^4 -10x^2+25

Answer 2

       

     Q ( X) =  X²  - 5 

 

     [ Q( x )] ²  = ( X ² - 5 ) ²  = X⁴  - 10 X²  + 25

 

    Using identity : ( X ± Y )²  = X²  ±2 XY + Y ²