Question
Factorise :$a^6- b^6$
✓
Answer
We know that,
$a^3 + b^3 = ( a + b )( a^2 - ab + b^2 ) ....(1)$
$a^3 - b^3 = ( a - b )( a^2 + ab + b^2 ) ....(2)$
$a^6 - b^6$
$= ( a^3)^2 - (b^3)^2$
$= ( a^3 + b^3 )( a^3 - b^3 )$
$= ( a + b )( a^2 - ab + b^2 )( a - b )( a^2 + ab + b^2 )$
$[$ From$(1)$ and $(2) ]$
$= ( a + b )( a - b )( a^2 - ab + b^2 )( a^2 + ab + b^2 )$
$a^3 + b^3 = ( a + b )( a^2 - ab + b^2 ) ....(1)$
$a^3 - b^3 = ( a - b )( a^2 + ab + b^2 ) ....(2)$
$a^6 - b^6$
$= ( a^3)^2 - (b^3)^2$
$= ( a^3 + b^3 )( a^3 - b^3 )$
$= ( a + b )( a^2 - ab + b^2 )( a - b )( a^2 + ab + b^2 )$
$[$ From$(1)$ and $(2) ]$
$= ( a + b )( a - b )( a^2 - ab + b^2 )( a^2 + ab + b^2 )$
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