Question
Factorise : $(a + b)^3- a - b$
✓
Answer
$(a + b)^3 - a - b$
$= ( a + b )^3 - ( a + b )$
$= ( a + b )[ ( a + b )^2 - 1 ]$
$= ( a + b )[ ( a + b )^2 - (1)^2 ]$
$= ( a + b )[( a + b ) + 1 ][( a + b ) - 1] [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= ( a + b )( a + b + 1 )( a + b - 1 )$
$= ( a + b )^3 - ( a + b )$
$= ( a + b )[ ( a + b )^2 - 1 ]$
$= ( a + b )[ ( a + b )^2 - (1)^2 ]$
$= ( a + b )[( a + b ) + 1 ][( a + b ) - 1] [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= ( a + b )( a + b + 1 )( a + b - 1 )$
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