Question

(1+a) (1+a²) (1+a⁴) (1-a) (1+a8) equals...... details ​

Answer 1

Answer:

             1 - a¹⁶

Step-by-step explanation:

Repeatedly use the difference of squares factorization:

• (x + y) (x - y)  =  x² - y²

So...

   (1 + a) (1 + a²) (1 + a⁴) (1 - a) (1 + a⁸)

=  (1 - a) (1 + a) (1 + a²) (1 + a⁴) (1 + a⁸)                [ just reordered the factors ]

=  (1 - a²) (1 + a²) (1 + a⁴) (1 + a⁸)                         [ did (1-a)(1+a) = 1-a² ]

=  (1 - a⁴) (1 + a⁴) (1 + a⁸)                                     [ did (1-a²)(1+a²) = 1-a⁴ ]

=  (1 - a⁸) (1 + a⁸)                                                 [ did (1-a⁴)(1+a⁴) = 1-a⁸ ]

=  1 - a¹⁶