Factorise the following: x 2 + xy(1 + y) + y 3

x 2 + xy(1 + y) + y 3 = x 2 + xy + xy 2 + y 3 = x(x + y) + y 2 (x + y) = (x + y)(x + y 2 ). Hence, x 2 + xy(1 + y) + y 3 = (x + y)(x + y 2 ).

Mathematics

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x² + xy(1 + y) + y³

= x² + xy + xy² + y³

= x(x + y) + y²(x + y)

= (x + y)(x + y²).

Hence, x² + xy(1 + y) + y³ = (x + y)(x + y²).

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