What is the value of the following expression ?(1 + x)(1 + x2)(1 + x4)

1.	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» (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)

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»

(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)