Long division

Question

Hi, what are the steps in solving the following using long division : 

 

a³+b³ / a+b 

Answer 1

 

a³ + b³ can be factored using the sum of cubes rule

 

     a³ + b³ = (a + b)(a² - ab + b²)

 

So when we substitute into the original problem,

 

    a³ + b³

    ------------

     a + b

 

    (a + b)(a² -ab + b²)

=-------------------------------

     (a + b)

 

The a + b in the numerator and denominator will cancel themselves out ... (a+b) divided by (a+b) = 1

 

So the answer is  ... a² -ab + b²

Answer 2

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Answer 3

            a²  - ab + b²

a + b | a^{3  +   0   +  0}     + b³

           a³ + a²b

                -a²b

                -a²b - ab²

                          ab² + b³