Question

1) Using identity find the product: (x-1)(x+1)(x^2+1)(x^4+1)

Answer 1

=(x-1)(x+1)(x^2+1)(x^4+1)

[using identity:a^2-b^2=(a+b)(a-b)]

=[(x-1)(x+1)](x^2+1)(x^4+1)

=(x^2-1)(x^2+1)(x^4+1)

=[(x^2-1)(x^2+1)](x^4+1)

=(x^4-1)(x^4+1)

=x^8-1(ans)

Answer 2

The answer is (x⁸-1)

Given : The given mathematical problem is, (x-1)(x+1)(x^2+1)(x^4+1)

To find : The product.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the product)

The mathematical problem :

= (x-1) (x+1) (x²+1) (x⁴+1)

Here, we cannot just manually evaluate the final result. We have to use suitable identities.

So,

= (x-1) (x+1) (x²+1) (x⁴+1)

= [(x-1) (x+1)] (x²+1) (x⁴+1)

= [(x)²-(1)²] (x²+1) (x⁴+1)

= (x²-1) (x²+1) (x⁴+1)

= [(x²-1) (x²+1)] (x⁴+1)

= [(x²)²-(1)²] (x⁴+1)

= (x⁴-1) (x⁴+1)

= (x⁴)²-(1)²

= (x⁸-1)

(This will be considered as the final result.)

Hence, the answer is (x⁸-1)