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Plus de krusangduan54 (10)
Math11
- 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 4
5. (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. 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