The absolute difference of the coefficients of x 10 and x 7 in the expansion of 2 x 2 + 1 2 x 11 is equal to

Step-by-step solution

The given expansion is 2 x 2 + 1 2 x 11 . The general term in the binomial expansion of x + a n is given by T r + 1 = C r n x n - r a r . ⇒ T r + 1 = C r 11 2 x 2 11 - r 1 2 x r = C r 11 2 11 - r - r x 22 - 2 r - r Now for coefficient of x 7 ⇒ 22 - 3 r = 7 ⇒ r = 5 Coefficient of x 7 is C 5 11 2 11 - 5 × 2 Now for coefficient of x 10 ⇒ 22 - 3 r = 10 ⇒ r = 4 Coefficient of x 10 is C 4 11 2 11 - 2 × 4 We need the absolute difference, we get it by C 5 11 2 11 - 5 × 2 - C 4 1