factories : a^3 +3ab +1
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We know that,
a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ca)
Now, a³ + b³ + 3ab - 1
= a³ + b³ - 1 + 3ab
= a³ + b³ + (- 1)³ - 3ab(- 1)
= (a + b - 1) {a² + b² + (- 1)² - ab - b(- 1) - (- 1)a}
= (a + b - 1) (a² + b² + 1 - ab + b + a),
which is the required factorization.
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Step-by-step explanation:
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