Algebric Operations
( Algebric Operations ) प्रमुख सूत्र ( Important Formulae )
( a + b ) 2 = a2+ 2ab + b2 = ( a – b )2 + 4ab
( a – b ) 2 = a2 – 2ab + b2 = ( a + b )2 – 4ab
( a + b )2 + ( a – b ) 2 = 2 ( a² + b2 )
( a + b ) 2 – ( a – b ) 2 = 4ab
A2 + b2 = ( a + b ) 2 – 2ab = ( a – b ) 2 + 2ab
A2 – b2 = ( a + b ) ( a – b )
( a + b + c ) 2 = a + b2 + 2 + 2ab + bc + ca ) = a + b2 +c2 + 2ab + 2bc + 2ca
( a + b -c ) 2 = a2 + b2+ c2 + 2ab – 2bc – 2ca
( a – b + c ) 2 = a + b + c2 – 2ab – 2bc + 2ca
( -a + b + c ) 2 = a2 + b2 + c2 – 2ab + 2bc – 2ac
( a – b – c ) 2 = a 2 + b2+ c2 – 2ab + 2bc – 2ca
a+ b+c = ( a + b + c ) 2 – 2(ab + bc + ca ) = ( a + b + c ) 2 – 2ab – 2bc – 2ca
a 3 + b3 + c 3 – ab – bc – ca = 3 [ ( a – b ) ² + ( 6 – c ) 2 + ( c – a ) 2 ]
( a + b + c + d ) 2 = a + b + c + d2 + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd
( a + b ) 3 = a3 + b3 + 3ab ( a + b ) = a3 + 3a²b + 3ab + b3
( a – b ) = a 3 – b3 – 3ab ( a – b ) = a 3– 3a + b + 3ab2 –
( a + b ) 3 + ( a – b ) 3 = 2a + 6ab2
( a + b ) 3 – ( a – b ) 3 = ab3 + 6a²b
a3 + b3 = ( a + b ) 3 – 3ab ( a + b ) = ( a + b ) ( a- ab + b )
a3 – b3 = ( a – b ) 2 + 3ab ( a – b ) = ( a – b ) ( a + ab + b) a +
a + b = a3 – ab + b2 a2-b3
a – b = a² + ab + b²
IF X+1/X = U
X2+1/X2 = U2 -2
X3 + 1/X3 = U3 -3U
X4 + 1/X4 = U4 -4U2+2
X5 + 1/X5 = U5 –5U3+5U
X6 + 1/X6 = U6-6U4+9U2-2
IF X-1/X = U
X2+1/X2 = U2 +2
X3 – 1/X3 = U3 +3U
X4 + 1/X4 = U4 +4U2+2
X5 – 1/X5 = U5 +5U3+5U
X6 + 1/X6 = U6+6U4+9U2+2