(a^2-b^2)^4 /(a^2+b^2)*(a^2-b^2)/(a+b)^4

asked by guest
on Nov 23, 2024 at 5:09 pm



You asked:

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

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{{\left( {a}^{2} - {b}^{2} \right)}^{4}}{{a}^{2} + {b}^{2}} \cdot \left({a}^{2} - {b}^{2}\right)}{{\left( a + b \right)}^{4}} = \frac{\left(a^{2} - b^{2}\right)^{5}}{\left(a^{2} + b^{2}\right) \left(a + b\right)^{4}} \)

Expanded

\[\frac{\frac{{\left( {a}^{2} - {b}^{2} \right)}^{4}}{{a}^{2} + {b}^{2}} \cdot \left({a}^{2} - {b}^{2}\right)}{{\left( a + b \right)}^{4}} = \frac{a^{10}}{a^{6} + 4 a^{5} b + 7 a^{4} b^{2} + 8 a^{3} b^{3} + 7 a^{2} b^{4} + 4 b^{5} a + b^{6}} - \frac{5 a^{8} b^{2}}{a^{6} + 4 a^{5} b + 7 a^{4} b^{2} + 8 a^{3} b^{3} + 7 a^{2} b^{4} + 4 b^{5} a + b^{6}} + \frac{10 a^{6} b^{4}}{a^{6} + 4 a^{5} b + 7 a^{4} b^{2} + 8 a^{3} b^{3} + 7 a^{2} b^{4} + 4 b^{5} a + b^{6}} - \frac{10 a^{4} b^{6}}{a^{6} + 4 a^{5} b + 7 a^{4} b^{2} + 8 a^{3} b^{3} + 7 a^{2} b^{4} + 4 b^{5} a + b^{6}} + \frac{5 a^{2} b^{8}}{a^{6} + 4 a^{5} b + 7 a^{4} b^{2} + 8 a^{3} b^{3} + 7 a^{2} b^{4} + 4 b^{5} a + b^{6}} - \frac{b^{10}}{a^{6} + 4 a^{5} b + 7 a^{4} b^{2} + 8 a^{3} b^{3} + 7 a^{2} b^{4} + 4 b^{5} a + b^{6}}\]

Factored

\[\frac{\frac{{\left( {a}^{2} - {b}^{2} \right)}^{4}}{{a}^{2} + {b}^{2}} \cdot \left({a}^{2} - {b}^{2}\right)}{{\left( a + b \right)}^{4}} = \frac{\left(a - b\right)^{5} \left(a + b\right)}{a^{2} + b^{2}}\]

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