If ' a ' is the middle term in the expansion of ( 2 x - 3 y ) 8 and b , c are the middle terms in the expansion of ( 3 x + 4 y ) 7 , then the value of b + c a , when x = 2 and y = 3 , is

Step-by-step solution

It is given that x = 2 ,   y = 3 By the expansion of ( 2 x - 3 y ) 8 middle term is 5 th  term. a = C 4 8 ( 2 x ) 4 ( 3 y ) 4 ( - 1 ) 4 ⇒ a = 8 ! 4 ! 4 ! × 2 4 × 3 4 × x 2 y 2 = 70 × 2 4 × 3 4 × 2 4 × 3 4 Similarly, in the expansion of ( 3 x + 4 y ) 7 ,   4 th and 5 th terms are middle terms. b = C 3 7 ( 3 x ) 4 ( 4 y ) 3 = 35 × 3 7 × 2 10 c = C 4 7 ( 3 x ) 3 ( 4 y ) 4 = 35 × 3 7 × 2 11 Now, b + c 2 = 35 × 3 7 × 2 10 + 35 × 3