Simplify the expression: $(2x+1)×\left(x^2+(x+1)^2 \right)×\left( (x^4+(x+1)^4) \right)×...×\left(x^{64}+(x+1)^{64}\right)$ Simplify the expression:
$$(2x+1)×\left(x^2+(x+1)^2 \right)×\left( (x^4+(x+1)^4) \right)×...×\left(x^{64}+(x+1)^{64}\right)$$
I used the general method:
$(2x+1)(2x^2+2x+1)(2x^4+4x^3+6x^2+4x+1)×...$
But, But I'm stuck here.

A method like this can work:

$$\left( x+1-x\right)×\left(x+1+x \right)×\left((x+1)^2+x^2 \right)×\left( (x+1)^4+x^4\right)×...×\left((x+1)^{64}+x^{64}\right)=(x+1)^{128}-x^{128}$$

