{b + x}{b^2 + bx + x^2} - \frac{2x^3}{b^4 + b^2x^2 + x^4}.

asked by guest
on Jan 24, 2025 at 11:10 am



You asked:

Evaluate the expression: \(\left(b + x\right) \left({b}^{2} + b x + {x}^{2}\right) - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}}\)

MathBot Answer:

Evaluated



\(\displaystyle \left(b + x\right) \left({b}^{2} + b x + {x}^{2}\right) - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}} = - \frac{2 x^{3}}{b^{4} + b^{2} x^{2} + x^{4}} + \left(b + x\right) \left(b^{2} + b x + x^{2}\right) \)

Expanded

\[\left(b + x\right) \left({b}^{2} + b x + {x}^{2}\right) - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}} = b^{3} + 2 b^{2} x + 2 x^{2} b + x^{3} - \frac{2 x^{3}}{b^{4} + b^{2} x^{2} + x^{4}}\]

Factored

\[\left(b + x\right) \left({b}^{2} + b x + {x}^{2}\right) - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}} = \frac{b^{7} + 2 b^{6} x + 3 b^{5} x^{2} + 3 b^{4} x^{3} + 3 b^{3} x^{4} + 3 b^{2} x^{5} + 2 x^{6} b + x^{7} - 2 x^{3}}{\left(b^{2} - b x + x^{2}\right) \left(b^{2} + b x + x^{2}\right)}\]

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