完全立方公式包括完全立方和公式和完全立方差公式 ( a ± b ) 3 = a 3 ± 3 a 2 b + 3 a b 2 ± b 3 (a±b)^3=a^3±3a^2b+3ab^2±b^3 (a±b)3=a3±3a2b+3ab2±b3
( a + b ) 3 = ( a + b ) ( a + b ) ( a + b ) = ( a 2 + 2 a b + b 2 ) ( a + b ) = a 3 + 3 a 2 b + 3 a b 2 + b 3 (a+b)^3=(a+b)(a+b)(a+b) = (a^2+2ab+b^2)(a+b)=a^3+3a^2b + 3ab^2+ b^3 (a+b)3=(a+b)(a+b)(a+b)=(a2+2ab+b2)(a+b)=a3+3a2b+3ab2+b3
( a − b ) ³ = ( a − b ) ( a − b ) ( a − b ) = ( a ² − 2 a b + b ² ) ( a − b ) = a ³ − 3 a ² b + 3 a b ² − b ³ (a-b)³=(a-b)(a-b)(a-b)=(a²-2ab+b²)(a-b)=a³-3a²b+3ab²-b³ (a−b)³=(a−b)(a−b)(a−b)=(a²−2ab+b²)(a−b)=a³−3a²b+3ab²−b³
a 3 + b 3 = ( a + b ) ( a 2 − a b + b 2 ) a^3+b^3=(a+b)(a^2-ab+b^2) a3+b3=(a+b)(a2−ab+b2)
a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 ) a^3-b^3=(a-b)(a^2+ab+b^2) a3−b3=(a−b)(a2+ab+b2)
1 3 + 2 3 + . . . n 3 = [ n ∗ ( n + 1 ) 2 ] 2 = ( 1 + 2 + . . n ) 2 1^3+2^3+...n^3=[\frac{n*(n+1)}{2}]^2=(1+2+..n)^2 13+23+...n3=[2n∗(n+1)]2=(1+2+..n)2
