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# Math11

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### Math11

1. 1. ! "# x , y ( )* n ( ,! ก )*# n n n n ( x + y) n =   ⋅ x n +   ⋅ x n −1 y + K +   ⋅ x n − r y r + K +   ⋅ y n 0 1 r n         1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 ก 1. ( 2 x + y)3  3  3  3  3 ( 2 x + y ) 3 =  ( 2 x ) 3 +  ( 2 x ) 2 ⋅ y +  ( 2 x ) ⋅ y 2 +   y 3  0 1  2  3         = 1 ⋅ 23 ⋅ x 3 + 3 ⋅ 2 2 ⋅ x 2 ⋅ y + 3 ⋅ 2 ⋅ x ⋅ y 2 + 1 ⋅ y 3 = 8x 3 + 12 x 2 y + 6 xy 2 + y 3 3  3  3  3 2. ( x − 2 y ) 3 =   x 3 +   x 2 ( −2 y ) +   x ⋅ ( −2 y ) 2 +   ( −2 y ) 3 0 1  2  3         = x 3 − 6 x 2 y + 12 xy 2 − 8 y 3  3  3  3  3 3. (a − 2 b ) 3 =  a 3 −  a 2 ( 2 b ) +  a ⋅ ( 2 b ) 2 −  ( 2 b ) 2 0 1  2  3         = a 3 − 6a 2 b + 12ab 2 − 8b 3 4. (a − b) 4 = a 4 − 4a 3b + 6a 2 b 2 − 4ab3 + b 45. (a − b)5 = a 5 − 5a 4 b + 10a 3b 2 − 10a 2 b 3 + 5ab 4 − b 5(a + b)6 = a 6 + 6a 5b + 15a 4 b 2 + 20a 3b3 + 15a 2 b 4 + 6ab5 + b 6( 2a + b ) 4 = ( 2a ) 4 + 4( 2a ) 3 b + 6( 2a ) 2 b 2 + 4( 2a ) b 3 + b 4 = 16a 4 + 32a 3b + 24a 2 b 2 + 8ab3 + b 4
2. 2. 15  3 1  2 - . / 0 !! x กก ก x + 2   x  n1 ก23 Tr +1 =   ⋅ a n − r ⋅ b r r   1 ) a = x 3 , b = 2 )* n = 15 4 23 x r 5# Tr +1 =   ⋅ ( x 3 )15−r ⋅  12  15   r     x  15   x 45−3r  =   ⋅  2r r  x       15  =   ⋅ x 45−5r   r 60 ก 7 / # ก - . / 0 !! x ก8 3 )25 45 − 5r = 0 5r = 45 r=9 15  5# T9+1 =   ⋅ x 45−5×9 9   15! T10 = (15 − 9)!⋅9! 15! = 6!⋅9! 15 ⋅ 14 ⋅ 13 ⋅ 12 ⋅ 11 ⋅ 9 = 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅1 = 5,005 . / 0 !! x ก8 3 96 . / 0 10 !9 ก: 5,005