factorise a³-b³+1+3ab
step by step with explaination pls
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Given : a³-b³+1+3ab
To Find : factorise
Solution:
Use the formula :
a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)
a³-b³+1+3ab
= a³ + (-b)³ + 1³ + 3(a) (b) (1)
= a³ + (-b)³ + 1³ - 3(a) (-b) (1)
= (a - b + 1) ( a² + b² + 1² - a(-b) - (-b)(1) - (1)a)
= (a - b + 1) ( a² + b² + 1 + ab + b - a)
a³-b³+1+3ab = (a - b + 1) ( a² + b² + 1 + ab + b - a)
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