Question

What is the value of the following expression ?

(1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)(1 - x)

(a) 1 + x¹⁶

(b) 1 - x¹⁶

(c) x¹⁶ - 1

(d) x⁸ + 1

Answer 1

(b) 1 + x¹⁶

(1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)(1 - x)

= (1 + x)(1 - x)(1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)

= (1 - x²)(1 + x²)(1 + x⁴)(1 + x⁸)

= (1 - x⁴)(1 + x⁴)(1 + x⁸)

= (1 - x⁸)(1 + x⁸) = (1 + x¹⁶)