What is (x+5)(x-5)(x^2+25)(x^4+625)+625^2 ?

The solution to (x+5)(x-5)(x^2+25)(x^4+625)+625^2 is x^8

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simplify (x+5)(x-5)(x^2+25)(x^4+625)+625^2

simplify

(x + 5) (x - 5) (x^{2} + 25) (x^{4} + 625) + 62 5^{2}

x^{8}

Solution steps

(x + 5) (x - 5) (x^{2} + 25) (x^{4} + 625) + 62 5^{2}

Expand

(x + 5) (x - 5) (x^{2} + 25) (x^{4} + 625) : x^{8} - 62 5^{2}

= x^{8} - 62 5^{2} + 62 5^{2}

Add similar elements:

- 62 5^{2} + 62 5^{2} = 0

= x^{8}

9 x^{2} + \frac{3}{2} x + \frac{1}{16}

(5 - - 9) (- 1 + - 4)

(3^{2})^{3} \cdot (2 \cdot 3^{5})^{- 2} \cdot (18)^{2}

1 - x^{8}

2 + \frac{1}{3 + \frac{1}{1 + \frac{1}{1 + \frac{1}{2}}}}

What is (x+5)(x-5)(x^2+25)(x^4+625)+625^2 ?
The solution to (x+5)(x-5)(x^2+25)(x^4+625)+625^2 is x^8