Answers

The Brainliest Answer!
2015-12-25T09:31:23+05:30
1) ( 2x - 1/2x )^6

You will get x^2 when { ( 2x )^4 * ( 1/2x)^2 } and

So { 6 C 4 } * 2^4 * ( 1/2)^2 = 15 * 16 * 1/4 = 15 * 4 = 60

2) ( 1 + x^2 ) ( 2x - 1/2x )^6

You will get x^2 when 1 multiples to a term having x^2 in tha expansion of ( 2x - 1/2x )^6 that we have already found in previous problem AND you will get x^2 when
x^2 from ( 1 + x^2 ) multiplies to a constant term in the other expansion which is when { (2x)^3 (-1/2x)^3 }

So coeffcient of x^2 = 60 ( from previous problem )+ coefficient of { (2x)^3 (-1/2x)^3 }
= 60 + 3 C 3 * 8 * ( -1/8 ) = 60-1 = 59
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