Question

Simplify: (1+a) (1+a²)(1+a⁴)(1-a)(1+a8)​

Answer 1

Answer:

$(1+a) (1+a²)(1+a⁴)(1-a)(1+a8)$

$= (1 - a ^{2} )(1 + a ^{2} )(1 + a ^{4} ) \\ (1 - a)(1 + a ^8 )$

$(1 - a ^{8} )(1 + a ^{8} )$

$= 1 - a ^{16}$

I hope this might help you with ☺

Answer 2

Answer:

The answer is $1-a^{16}$

Step-by-step explanation:

• Algebraic identity :$(a-b)(a+b)=a^2-b^2$

  Therefore  $(1+a)(1+a^2)(1+a^4)(1-a)(1+a^8)$

                   $=[(1-a)(1+a)](1+a^2)(1+a^4)(1+a^8)$

                   $=(1-a^2)(1+a^2)(1+a^4)(1+a^8)$ , using above formula

                   $=[(1-a^2)(1+a^2)](1+a^4)(1+a^8)\\=(1-a^4)(1+a^4)(1+a^8)$

                   $=[(1-a^4)(1+a^4)](1+a^8)\\=(1-a^8)(1+a^8)\\=1-a^{16}$