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Factorize the given term $a^{3} - b^{3} + 1 + 3 ab$ ?

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(a + b + 1) (a^{2} + b^{2} + 1 + ab + b + a)

(a + b - 1) (a^{2} + b^{2} + 1 - ab + b - a)

(a - b + 1) (a^{2} + b^{2} + 1 + ab + b - a)

(a - b - 1) (a^{2} + b^{2} + 1 - ab - b + a)

answer is C.

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Detailed Solution

x^{3} + y^{3} + z^{3} - 3 xyz = (x + y + z) (x^{2} + y^{2} + z^{2} - xy - yz - zx)

a^{3} - b^{3} + 1 + 3 ab = a^{3} + {(- b)}^{3} + 1^{3} - 3 a (- b) 1 = (a - b + 1) (a^{2} + b^{2} + 1 + ab + b - a)

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