CTET 2 Math and Science Sep 2014 Paper

Question : 39 of 120

Marks: +1, -0

If x is an integer, then

(x + l)^4 - (x – 1)^4

is always divisible by

Solution:

Given that

(x+1)^{4}-(x-1)^{4}

it can be written as

=((x+1)^{2}-(x-1)^{2})((x+1)^{2}+(x-1)^{2})

=(x^{2}+1+2x-x^{2}-1+2x)(x^{2}+1+2x+x^{2}+1-2x)

=4x×(2x^{2}+2)

=8x(x^{2}+1)

The whole term is multiple of 8.
Therefore, the number is also divisible by 8.

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