Find the 13th term of the binomial expansion of \((2x - 4)^{21}\).
Answer (2)
T r = ( r − 1 n ) a n − r + 1 b r − 1 T 13 = ( 13 − 1 21 ) ( 2 x ) 21 − 13 + 1 ( − 4 ) 13 − 1 T 13 = ( 12 21 ) ( 2 x ) 9 ( − 4 ) 12 T 13 = 12 ! 9 ! 21 ! ⋅ 512 x 9 ⋅ 16777216 T 13 = 293930 ⋅ 8589934592 x 9 T 13 = 2524839474626560 x 9
The 13th term of the binomial expansion of ( 2 x − 4 ) 21 is 1081222239490510 x 9 . This was found using the binomial theorem, calculating the binomial coefficient, the powers of the terms, and multiplying them together. The process involved setting the right values for the terms and calculating step by step.
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