Question

Factorise the following expressions. (a-b)²+(a-b) ​

Answer 1

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Answer 2

$(a - b)^{2} + (a - b) \\ = (a^{2} - 2ab + {b}^{2} ) + a - b \\ = a(a^{2} - 2ab + {b}^{2} ) \\ - b(a^{2} - 2ab + {b}^{2} )$

$= {a}^{3} - 2 {a}^{2} b + a {b}^{2} \\ - a^{2} b + 2a {b}^{2} - {b}^{3}$

$= {a}^{3} - 2 {a}^{2} b - {a}^{2}b \\ + ab^{2} + 2a {b}^{2} - {b}^{3} \\ = {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3}$