Question

Find $(a+b{)}^4-(a-b{)}^4$. Hence, evaluate $(\sqrt{3}+\sqrt{2}{)}^4-(\sqrt{3}-\sqrt{2}{)}^4.$

Answer 1

$(a+b{)}^4-(a-b{)}^4$

$=\left\{\right(a+b{)}^2-(a-b{)}^2\}$$\left\{\right(a+b{)}^2+(a-b{)}^2\}$

$=\left(4ab\right)\left\{2\right(a^2+b^2\left)\right\}$........(1)

Using (1) we get,

$(\sqrt{3}+\sqrt{2}{)}^4-(\sqrt{3}-\sqrt{2}{)}^4$

$=(4.\sqrt{3}.\sqrt{2})\left\{2\right(3+2\left)\right\}$

$=40\sqrt{6}$.