What is expand (2+sqrt(3))^{10}(2-sqrt(3))^{10} ?

The solution to expand (2+sqrt(3))^{10}(2-sqrt(3))^{10} is 1

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expand (2+sqrt(3))^{10}(2-sqrt(3))^{10}

expand

(2 + 3)^{10} (2 - 3)^{10}

1

Solution steps

(2 + 3)^{10} (2 - 3)^{10}

Expand

(2 + 3)^{10} : 1024 + 51203 + 34560 + 460803 + 120960 + 725763 + 90720 + 259203 + 14580 + 16203 + 243

= (1024 + 51203 + 34560 + 460803 + 120960 + 725763 + 90720 + 259203 + 14580 + 16203 + 243) (2 - 3)^{10}

= (2 - 3)^{10} (1024 + 51203 + 34560 + 460803 + 120960 + 725763 + 90720 + 259203 + 14580 + 16203 + 243)

Distribute parentheses

= (2 - 3)^{10} \cdot 1024 + (2 - 3)^{10} \cdot 51203 + (2 - 3)^{10} \cdot 34560 + (2 - 3)^{10} \cdot 460803 + (2 - 3)^{10} \cdot 120960 + (2 - 3)^{10} \cdot 725763 + (2 - 3)^{10} \cdot 90720 + (2 - 3)^{10} \cdot 259203 + (2 - 3)^{10} \cdot 14580 + (2 - 3)^{10} \cdot 16203 + (2 - 3)^{10} \cdot 243

(2 - 3)^{10} \cdot 1024 + (2 - 3)^{10} \cdot 51203 + (2 - 3)^{10} \cdot 34560 + (2 - 3)^{10} \cdot 460803 + (2 - 3)^{10} \cdot 120960 + (2 - 3)^{10} \cdot 725763 + (2 - 3)^{10} \cdot 90720 + (2 - 3)^{10} \cdot 259203 + (2 - 3)^{10} \cdot 14580 + (2 - 3)^{10} \cdot 16203 + (2 - 3)^{10} \cdot 243 = 262087 (2 - 3)^{10} + 1513163 (2 - 3)^{10}

= 262087 (2 - 3)^{10} + 1513163 (2 - 3)^{10}

Expand

262087 (2 - 3)^{10} : 68689595569 - 396579564923

= 68689595569 - 396579564923 + 1513163 (2 - 3)^{10}

Expand

1513163 (2 - 3)^{10} : 396579564923 - 68689595568

= 68689595569 - 396579564923 + 396579564923 - 68689595568

68689595569 - 396579564923 + 396579564923 - 68689595568 = 1

= 1

(x^{3} + 3 x y^{2}) d x + (y^{3} + 3 x^{2} y) d y

(2 - π)^{2}

z^{2} (\frac{z}{z - 3} - 1 - \frac{3}{z})

(A x + B) (A x sin (x) + B x cos (x))

\frac{1 - x ^{2} cos ( x )}{( 1 + x sin ( x ) ) ^{2}}

What is expand (2+sqrt(3))^{10}(2-sqrt(3))^{10} ?
The solution to expand (2+sqrt(3))^{10}(2-sqrt(3))^{10} is 1