Question number 16 Please give a shortcut method (if any) Q16 The continued product of (1 - Maths - Direct and Inverse Proportions

Question

Question number 16 Please give a shortcut method (if
any)

Q16 The continued product of (1 + x) , (1 + x2) , (1 +
x4), (1 + x8 ) and ( 1 – x ) is :

(A) ( 1 – x16 ) (B) ( x16 –
1)

(C) ( 1 – x8 + x16) (D) ( x8 +
x16 )

Sanjari Kalantri · Accepted Answer

Dear Student,

We use the identity a2 - b2 = (a + b)(a - b) repeatedly to solve the given question
(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)

Question number 16. Please give a shortcut method (if any). Q16. The continued product of (1 + x) , (1 + x2) , (1 + x4), (1 + x8 ) and ( 1 – x ) is : (A) ( 1 – x16 ) (B) ( x16 – 1) (C) ( 1 – x8 + x16) (D) ( x8 + x16 )

Question number 16. Please give a shortcut method (if any).

Q16. The continued product of (1 + x) , (1 + x²) , (1 + x⁴), (1 + x⁸ ) and ( 1 – x ) is :

(A) ( 1 – x¹⁶ ) (B) ( x¹⁶ – 1)

(C) ( 1 – x⁸ + x¹⁶) (D) ( x8 + x¹⁶ )