Question
Factorise the following by the difference of two squares:$a(a - 1) - b(b - 1)$
✓
Answer
$a(a - 1) - b(b - 1)$
$a^2 - a - b^2 + b$
$= a^2 - b^2 - a + b$
$= (a^2 - b^2) - (a - b)$
$= (a - b)(a + b) - (a - b)$
$= (a - b)(a + b - 1).$
$a^2 - a - b^2 + b$
$= a^2 - b^2 - a + b$
$= (a^2 - b^2) - (a - b)$
$= (a - b)(a + b) - (a - b)$
$= (a - b)(a + b - 1).$
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