Use the Binomial Theorem to find the coefficient of x^7 in the expansion of (x-2)^(11).

django0a6

django0a6

Answered question

2022-11-03

Use the Binomial Theorem to find the coefficient of x 7 in the expansion of ( x 2 ) 11 ?

Answer & Explanation

Eynardfb0

Eynardfb0

Beginner2022-11-04Added 19 answers

Binomial expansion of
( x + y ) n = k = 0 n ( n k ) x n k y k ( x 2 ) 11 = k = 0 11 ( 11 k ) x 11 k ( 2 ) k 11 k = 7 x 11 k = x 7 k = 11 7 k = 4
So coefficient of x 7 is
( 11 4 ) ( 2 ) 4 = ( 11 ) ! 4 ! ( 11 4 ) ! ( 2 ) 4 = ( 11 ) ! 4 ! ( 7 ) ! 2 4 = 11 × 10 × 9 × 8 × 7 ! 4 × 3 × 2 × 7 ! 2 4 = 11 × 10 × 3 ( 2 4 ) = 330 ( 16 ) = 5280

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