(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: (a2−b2)4a2+b2(a2−b2)(a+b)4\frac{\frac{{\left( {a}^{2} - {b}^{2} \right)}^{4}}{{a}^{2} + {b}^{2}} \left({a}^{2} - {b}^{2}\right)}{{\left( a + b \right)}^{4}}

MathBot Answer:

Evaluated



(a2−b2)4a2+b2(a2−b2)(a+b)4=(a2−b2)5(a2+b2)(a+b)4\displaystyle \frac{\frac{{\left( {a}^{2} - {b}^{2} \right)}^{4}}{{a}^{2} + {b}^{2}} \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

(a2−b2)4a2+b2(a2−b2)(a+b)4=a10a6+4a5b+7a4b2+8a3b3+7a2b4+4b5a+b6−5a8b2a6+4a5b+7a4b2+8a3b3+7a2b4+4b5a+b6+10a6b4a6+4a5b+7a4b2+8a3b3+7a2b4+4b5a+b6−10a4b6a6+4a5b+7a4b2+8a3b3+7a2b4+4b5a+b6+5a2b8a6+4a5b+7a4b2+8a3b3+7a2b4+4b5a+b6−b10a6+4a5b+7a4b2+8a3b3+7a2b4+4b5a+b6\frac{\frac{{\left( {a}^{2} - {b}^{2} \right)}^{4}}{{a}^{2} + {b}^{2}} \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

(a2−b2)4a2+b2(a2−b2)(a+b)4=(a−b)5(a+b)a2+b2\frac{\frac{{\left( {a}^{2} - {b}^{2} \right)}^{4}}{{a}^{2} + {b}^{2}} \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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