The term independent of x in the binomial expansion of 1 - 1 x + 3 x 5   2 x 2 - 1 x 8 is

Question

The term independent of x in the binomial expansion of 1 - 1 x + 3 x 5 &#160; 2 x 2 - 1 x 8 is

Aicharya · Accepted Answer

The term independent of x will come from 1 - 1 x + 3 x 5 2 x 2 - 1 x 8 General term of 2 x 2 - 1 x 8 is C 8 r ( &#8722; 1 x ) r &#160; 2 x 2 8 - r = C 8 r 2 8 &#8722; r ( &#8722; 1 ) r x 16 &#8722; 3 r From expansion 1 2 x 2 - 1 x 8 - 1 x 2 x 2 - 1 x 8 + 3 x 5 2 x 2 - 1 x 8 1 2 x 2 - 1 x 8 &#8594; no constant term - 1 x 2 x 2 - 1 x 8 &#8594; for constant term &#160; r = 5 &#160; &#160; &#8658; &#8722; C 8 3 2 3 ( &#8722; 1 ) 5 = + 448 3 x 5 2 x 2 - 1 x 8 &#8594; for constant term r = 7 &#8658; C 38 7 2 1 ( &#8722; 1 ) 7 = 48 Hence, term independent from x = 448 - 48 = 400

The term independent of x in the binomial expansion of 1 - 1 x + 3 x 5 &#160; 2 x 2 - 1 x 8 is

Solution

The term independent of x in the binomial expansion of 1 - 1 x + 3 x 5 2 x 2 - 1 x 8 is