What is (x^2-sqrt(2)x+1)(x^2+sqrt(2)x+1) ?

The solution to (x^2-sqrt(2)x+1)(x^2+sqrt(2)x+1) is x^4+1

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simplify (x^2-sqrt(2)x+1)(x^2+sqrt(2)x+1)

simplify

(x^{2} - 2 x + 1) (x^{2} + 2 x + 1)

x^{4} + 1

Solution steps

(x^{2} - 2 x + 1) (x^{2} + 2 x + 1)

Distribute parentheses

= x^{2} x^{2} + x^{2} 2 x + x^{2} \cdot 1 - 2 x x^{2} - 2 x 2 x - 2 x \cdot 1 + 1 \cdot x^{2} + 1 \cdot 2 x + 1 \cdot 1

Simplify

x^{2} x^{2} + x^{2} 2 x + x^{2} \cdot 1 - 2 x x^{2} - 2 x 2 x - 2 x \cdot 1 + 1 \cdot x^{2} + 1 \cdot 2 x + 1 \cdot 1 : x^{4} + 1

= x^{4} + 1

(2 a - \frac{1}{b})^{4}

\frac{6 ( s + 2 )}{( s + 1 ) ( s + 3 ) ( s + 4 )}

(x + 5 - 1)^{2}

\frac{s ^{2} + s + 3}{( s - 1 ) ( s + 2 ) ( s + 3 )}

1 - cos (2 x)

What is (x^2-sqrt(2)x+1)(x^2+sqrt(2)x+1) ?
The solution to (x^2-sqrt(2)x+1)(x^2+sqrt(2)x+1) is x^4+1