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