Suku yang bebas p pada penjabaran ( 2 p + p 2 3 ​ ) 12 adalah ...

Pembahasan

Rumus Binomial Newton adalah sebagai berikut. ( a + b ) n = i = 0 ∑ n ​ ( n i ​ ) a ( n − i ) b i Dengan a = 2 p b = p 2 3 ​ Maka, i = 0 0 ! ( 12 − 0 ) ! 12 ! ​ ( 2 p ) 12 ( p 2 3 ​ ) 0 ​ = = = = = ​ 0 ! ( 12 − 0 ) ! 12 ! ​ ( 2 p ) 12 ⋅ 1 0 ! ( 12 − 0 ) ! 12 ! ​ ( 2 p ) 12 12 ! 12 ! ​ ⋅ ( 2 p ) 12 1 ⋅ 2 12 p 12 4.096 p 12 ​ i = 1 1 ! ( 12 − 1 ) ! 12 ! ​ ( 2 p ) 11 ( p 2 3 ​ ) 1 ​ = = = = = = = ​ 1 ! ⋅ + 4 m u 11 ! 12 ! ​ ( 2 p ) 11 ( p 2 3 ​ ) 11 ! 12 ⋅ 11 ! ​ ⋅ 2 11 p 11 ⋅ ( p 2 3 ​ ) p 2 12 ⋅ + 4 m u 3 ⋅ + 4 m u 2 11 p 11 ​ 2 11 ⋅ + 4 m u 36 p 11 − 2 2 11 ⋅ 3 6 9 2.048 ⋅ + 4 m u 36 p 9 73.728 p 9 ​ i = 2 2 ! ( 12 − 2 ) ! 12 ! ​ ( 2 p ) 10 ( p 2 3 ​ ) 2 ​ = = = = = = = = ​ 2 ! ⋅ + 4 m u 10 ! 12 ! ​ 2 ! ⋅ + 4 m u 10 ! 12 ⋅ 11 ⋅ 10 ! ​ ⋅ 2 10 ⋅ p 10 ⋅ ( p 2 3 ​ ) 2 2 ! 12 ⋅ + 4 m u 11 ​ ⋅ 2 10 ⋅ p 10 ⋅ ( p 4 3 2 ​ ) 2 ! 12 ⋅ + 4 m u 11 ​ ⋅ p 4 132 ⋅ + 4 m u 3 2 ⋅ + 4 m u 2 10 p 10 ​ 2 ! 2 10 ⋅ + 4 m u 3 2 ⋅ + 4 m u 132 p 10 − 4 ​ 2 ⋅ 1 1.024 ⋅ 9 ⋅ 132 p 6 ​ 2 1.216.512 p 6 ​ 606.256 p 6 ​ i = 3 3 ! ( 12 − 3 ) ! 12 ! ​ ( 2 p ) 9 ( p 2 3 ​ ) 3 = 3 ! ⋅ + 4 m u 9 ! 12 ! ​ ⋅ 2 9 p 9 ⋅ p 6 3 3 ​ p 9 = 3 ! ⋅ 9 ! 12 ⋅ + 4 m u 11 ⋅ + 4 m u 10 ⋅ 9 ! ​ ⋅ 2 9 p 9 ⋅ p 6 3 3 ​ p 9 = 3 ! 12 ⋅ + 4 m u 11 ⋅ + 4 m u 10 ​ ⋅ ⋅ 2 9 p 9 ⋅ p 6 3 3 ​ p 9 = 3 ! p 6 1.320 ⋅ + 4 m u 3 3 ⋅ + 4 m u 2 9 p 9 ​ = 3 ! 2 9 ⋅ + 4 m u 3 3 ⋅ + 4 m u 1.320 p 9 − 6 ​ = 3 ! 2 9 ⋅ + 4 m u 3 3 ⋅ + 4 m u 1.320 p 3 ​ = 3 ⋅ 2 ⋅ 1 512 ⋅ 27 ⋅ 1.320 p 2 ​ = 6 18.247.680 p 3 ​ = 3.041.280 p 3 i = 4 4 ! ( 12 − 4 ) ! 12 ! ​ ( 2 p ) 8 ( p 2 3 ​ ) 4 ​ = = = = = = = = = ​ 4 ! ( 12 − 4 ) ! 12 ! ​ ⋅ 2 8 p 8 ⋅ ( p 2 ) 4 3 4 ​ 4 ! ⋅ + 4 m u 8 ! 12 ! ​ ⋅ 2 8 p 8 ⋅ p 8 3 4 ​ 4 ! ⋅ 8 ! 12 ⋅ + 4 m u 11 ⋅ + 4 m u 10 ⋅ + 4 m u 9 ⋅ 8 ! ​ ⋅ 2 8 p 8 ⋅ p 8 3 4 ​ 4 ! 12 ⋅ + 4 m u 11 ⋅ + 4 m u 10 ⋅ + 4 m u 9 ​ ⋅ 2 8 p 8 ⋅ p 8 3 4 ​ 4 ! 11.880 ​ ⋅ 2 8 ⋅ p 8 3 4 ​ p 8 4 ⋅ 3 ⋅ 2 ⋅ 1 11.880 ​ ⋅ 2 8 ⋅ p 8 ​ 3 4 ​ p 8 ​ 24 11.880 ​ ⋅ 256 ⋅ 81 495 ⋅ 256 ⋅ 81 10.264.320 ​ Jadi, suku yang bebas p pada penjabaran ( 2 p + p 2 3 ​ ) 12 adalah . Oleh karena itu, jawaban yang tepat adalah C.