Factorise:
$a^{2} + a b (b + 1) + b^{3}$

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Solution

a² + ab (b + 1) + b³

a² + ab (b + 1) + b³

= a² + ab² + ab + b³

= a² + ab + ab² + b³

= a (a + b) + b² (a + b)

= (a + b) (a + b²)

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