Select the correct product. (x 2 + 4x + 8)(2x - 1) 2x3 + 7x2 + 12x - 8 2x3 - 7x2 - 12x - 8 x2 + 6x + 7 x2 + 8x - 8

The correct answer is:  [A]:  " 2x³  +  7x² + 12x − 8 " .


Explanation:

Given:  

" (x² + 4x + 8) (2x − 1) "  ;  Find the product: 

↔  " (2x − 1) (x² + 4x + 8) "  ; 


Note:  " (a + b) (c + d + e) = ab + ad + ae + bc + bd + ae " .


  →  " (2x − 1) (x² + 4x + 8) = 

      (2x * x²) + (2x * 4x) + (2x *8)  + (-1 * x²) + (-1 * 4x) + (-1 * 8) ; 

 =    2x³ + 8x² + 16x + (-1x²) + (-4x) + (-8) ; 

=     2x³ + 8x² + 16x − x² − 4x − 8) ; 

→ Combine the "like terms" :

        + 8x² − x² =  + 7x² ; 

        + 16x − 4x =  + 12x ; 

And rewrite the expression:

   →  " 2x³  +  7x² + 12x − 8 " ;

   → which is:  Answer choice:  [A]:  " 2x³  +  7x² + 12x − 8 " .