Q. 2 H4.4( 8 Votes )

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Answer :

In given expression


Take out the common factor,


[2 × x - 2 × 2 × 2 × 2 × 2 × x × x × x × x × x]


2 × x[1 - 2 × 2 × 2 × 2 × x × x × x × x]


2x [1-16x4] = 2x [1-(2x)4]


In the term 1-(2x)4


= 1-(4x2)2


Both terms are perfect square


(4x2 )2 = 4x2 × 4x2


1 = 1 × 1


1-(4x2)2 Seems to be in identity a2-b2 = (a + b)(a-b)


Where a = 1 and b = 4x2;


1-16x4 = (1-4x2)(1 + 4x2)


1-4x2 = 1-(2x)2


1-4x2 Seems to be in identity a2-b2 = (a + b)(a-b)


Where a = 1 and b = 2x;


1-4x2 = (1-2x)(1 + 2x)


1-16x2 = (1-2x)(1 + 2x) (1 + 4x2)


Hence the factors of 2x – 32x5 are 2x,(1-2x),(1 + 2x) and (1 + 4x2)


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