Question

simplify (1-x)(1+x)(1+x^2)(1+x^4)​

Answer 1

Answer:

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

=(1-x^8)

Answer 2

Answer:

There is an equation in Mathematics which goes by (a-b) (a+b) = a^2 - b^2,

So using this equation we can simplify the given problem.

First,

(1-x) (1+x) will become (1-x^2).

Now we have,

(1-x^2) (1+x^2) which will be (1-x^4).

Finally,

(1-x^4)(1+x^4) gives (1-x^8).

So it's down to (1-x^8).

As the degree of x is 8 hence, we will get 8 roots (values) of x which satisfies this equation.

Let’s equate the equation with zero,

1-x^8 = 0,

x^8 = 1

Hence x = (1,-1,1,-1,1,-1,1,-1).