Question

factorise a³-b³+1+3ab

step by step with explaination pls​

Answer 1

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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