What is expand (e+f+sqrt(e^4+f^4))(e+f-sqrt(e^4+f^4)) ?

The solution to expand (e+f+sqrt(e^4+f^4))(e+f-sqrt(e^4+f^4)) is 2ef+f^2-f^4-e^4+e^2

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expand (e+f+sqrt(e^4+f^4))(e+f-sqrt(e^4+f^4))

expand

(e + f + e^{4} + f^{4}) (e + f - e^{4} + f^{4})

2 e f + f^{2} - f^{4} - e^{4} + e^{2}

Solution steps

(e + f + e^{4} + f^{4}) (e + f - e^{4} + f^{4})

Distribute parentheses

= ee + e f + e (- e^{4} + f^{4}) + f e + ff + f (- e^{4} + f^{4}) + e^{4} + f^{4} e + e^{4} + f^{4} f + e^{4} + f^{4} (- e^{4} + f^{4})

Apply minus-plus rules

+ (- a) = - a

= ee + e f - e e^{4} + f^{4} + e f + ff - f e^{4} + f^{4} + e e^{4} + f^{4} + f e^{4} + f^{4} - e^{4} + f^{4} e^{4} + f^{4}

Simplify

ee + e f - e e^{4} + f^{4} + e f + ff - f e^{4} + f^{4} + e e^{4} + f^{4} + f e^{4} + f^{4} - e^{4} + f^{4} e^{4} + f^{4} : 2 e f + f^{2} - f^{4} - e^{4} + e^{2}

= 2 e f + f^{2} - f^{4} - e^{4} + e^{2}

a^{2 (n + 1)} - 2 a^{n + 1} b^{n - 1} + 120 b^{2 (n - 1)}

(3 ln (x) + 3 C)^{2}

(- \frac{3}{x})^{2}

(2.001)^{4}

\frac{2 x ( 6 - 2 x ) ^{3}}{3}

What is expand (e+f+sqrt(e^4+f^4))(e+f-sqrt(e^4+f^4)) ?
The solution to expand (e+f+sqrt(e^4+f^4))(e+f-sqrt(e^4+f^4)) is 2ef+f^2-f^4-e^4+e^2