solve: a^6+2a^3b^3-3b^6 divided by (a^3-b^3)

asked by guest
on Jan 19, 2025 at 5:22 am



You asked:

Evaluate the expression: \({a}^{6} + 2 {a}^{3} {b}^{3} - \frac{3 {b}^{6}}{{a}^{3} - {b}^{3}}\)

MathBot Answer:

Evaluated



\(\displaystyle {a}^{6} + 2 {a}^{3} {b}^{3} - \frac{3 {b}^{6}}{{a}^{3} - {b}^{3}} = a^{6} + 2 a^{3} b^{3} - \frac{3 b^{6}}{a^{3} - b^{3}} \)


Expanded

\[{a}^{6} + 2 {a}^{3} {b}^{3} - \frac{3 {b}^{6}}{{a}^{3} - {b}^{3}} = a^{6} + 2 a^{3} b^{3} - \frac{3 b^{6}}{a^{3} - b^{3}}\]


Factored

\[{a}^{6} + 2 {a}^{3} {b}^{3} - \frac{3 {b}^{6}}{{a}^{3} - {b}^{3}} = \frac{a^{9} + a^{6} b^{3} - 2 a^{3} b^{6} - 3 b^{6}}{\left(a - b\right) \left(a^{2} + a b + b^{2}\right)}\]