Đáp án:
$-2+4\sqrt{3}$
Giải thích các bước giải:
$\left(\sqrt{5}+\sqrt{3}-2\right)\cdot \left(\sqrt{5}-\sqrt{3}+2\right)$
$=\sqrt{5}\sqrt{5}+\sqrt{5}\left(-\sqrt{3}\right)+\sqrt{5}\:.\:\:2+\sqrt{3}\sqrt{5}+\sqrt{3}\left(-\sqrt{3}\right)+\sqrt{3}\:.\:\:2-2\sqrt{5}-2\left(-\sqrt{3}\right)-2\:.\:2$
$=\sqrt{5}\sqrt{5}+\sqrt{5}\left(-\sqrt{3}\right)+\sqrt{3}\sqrt{5}+\sqrt{3}\left(-\sqrt{3}\right)+\sqrt{3}\:.\:2-2\left(-\sqrt{3}\right)-2\:.\:\:2$
$=5-\sqrt{15}+\sqrt{15}-3+\sqrt{3}\:.\:2-\left(-2\sqrt{3}\right)-4$
$=5-\sqrt{15}+\sqrt{15}-3+\sqrt{3}\:.\:\:2+2\sqrt{3}-4$
$=5-3+\sqrt{3}\:.\:\:2+2\sqrt{3}-4$
$=-2+\sqrt{3}\:.\:\:2+2\sqrt{3}$
$=-2+4\sqrt{3}$
