SSC CHSL Model Paper 11

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Question : 58 of 100

Marks: +1, -0

What is the simplified value of

(x^128 + 1) (x^32 + 1) (x^64 + 1)

(x^16 + 1) (x^8 + 1)

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

?

$x^256-1$
${x^128-1}/{x-1}$
${x^64-1}/{x-1}$
${x^256-1}/{x-1}$

Solution:

Expression

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

.... (x^128 + 1)

= {(x-1)(x + 1) (x^2 + 1) (x^4 + 1) .... (x^128 + 1)}/(x-1)

= {(x^2-1) (x^2 + 1) (x^4 + 1) .... (x^128 + 1)}/(x-1)

= {(x^4-1) (x^4 + 1) (x^8 + 1).... (x^128 + 1)}/(x-1)

= {(x^8-1) (x^8 + 1) .... (x^128 + 1)}/(x-1)

............
............

={(x^128-1)(x^128+1)}/{x-1}

={x^256-1}/{x-1}

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