tính nhanh :
47^3 +9.47^2 +27.47 +27
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a) ( 100 + 1 ) 3 = 100 3 + 3 . 100 2 + 3.100 + 1 = 1030301.
b) ( 47 + 3 ) 3 = 50 3 = 125000.
c) ( 300 – 1 ) 3 = 26730899.
d) ( 1008 – 23 ) 3 = 1000 3 = 10 9 .
(145 x 99 + 145 ) - ( 143 x 102 – 143 × 2 ) + 54 x 47 - 47 x 53 - 20 - 27
= 145 × (99 + 1) – 143 × (102 – 2) + 47 × (54 – 53) – (20 + 27)
= 145 × 100 – 143 × 100 + 47 × 1 – 47
= 100 × (145 – 143) + (47 – 47)
= 100 × 2 + 0
= 200
(145 x 99 + 145 ) - ( 143 x 102 – 143 × 2 ) + 54 x 47 - 47 x 53 - 20 - 27
= 145 × (99 + 1) – 143 × (102 – 2) + 47 × (54 – 53) – (20 + 27)
= 145 × 100 – 143 × 100 + 47 × 1 – 47
= 100 × (145 – 143) + (47 – 47)
= 100 × 2 + 0
= 200
a/ \(=47^3+3.47^2.3+3.47.3^2+3^3\)
\(=\left(47+3\right)^3=50^3=125000\)
b/ \(=102^3-3.102^2.2+3.102.2^2-2^3\)
\(=\left(102-2\right)^3=100^3=1000000\)
(145 x 99 + 145 ) - ( 143 x 102 – 143 × 2 ) + 54 x 47 - 47 x 53 - 20 - 27
= 145 × (99 + 1) – 143 × (102 – 2) + 47 × (54 – 53) – (20 + 27)
= 145 × 100 – 143 × 100 + 47 × 1 – 47
= 100 × (145 – 143) + (47 – 47)
= 100 × 2 + 0
= 200
= 145 x (99+1) - 143 x ( 102-2) + 47 x ( 54 - 53) -20-27
= 145 x 100 - 143 x 100 + 47 x 1 -20-27
= 100 x ( 145 - 143 ) + 47 - 20 - 27
= 200 + 47 - 20 - 27
= 200
473 + 9.472 + 27.47 + 27
= 473 + 3.472.3 + 3.47.32 + 33
= ( 47 + 3 )3 ( HĐT số 4 )
= 503 = 125 000