MODERATE EXERCISES - Symbol Manipulation

(2) Expand each product.

 (a) (2x - 5)(x2 - x - 1)

 (b) (x2 - (sqrt(2))(x) + 1 )(x2 + (sqrt(2))(x) + 1 )

 

 (a) (2x - 5)(x2 - x - 1)
     2x3 - 2x2 - 2x - 5x2 + 5x + 5
     2x3 - 7x2 + 3x + 5

 (b) (x2 - (sqrt(2))(x) + 1 )(x2 + (sqrt(2))(x) + 1 )
     
      x4 + (sqrt(2))(x3) + x2 - (sqrt(2))(x3) - [(sqrt(2))x]2
            - (sqrt(2))x + x2 + (sqrt(2))x + 1

      x4 + 2x2 - 2x2 + 1
      x4 + 1