Question

Factorise : $2\sqrt{2}{x}^3+3\sqrt{3}{y}^3+\sqrt{5}(5-3\sqrt{6}xy)$

• A. $(\sqrt{2}x-\sqrt{3}y-\sqrt{5})(2x^2+3y^2+5-\sqrt{6}xy-\sqrt{5}y-\sqrt{10}x)$
• B. $(\sqrt{2}x+\sqrt{3}y-\sqrt{5})(2x^2+3y^2+5-\sqrt{6}xy-\sqrt{5}y-\sqrt{10}x)$
• C. $(\sqrt{2}x+\sqrt{3}y+\sqrt{5})(2x^2+3y^2+5-\sqrt{6}xy-\sqrt{5}y-\sqrt{10}x)$
• D. $(\sqrt{2}x+\sqrt{3}y+\sqrt{5})(2x^2-3y^2+5-\sqrt{6}xy-\sqrt{5}y-\sqrt{10}x)$

Answer 1

Answer: (C)

$(\sqrt{2}x+\sqrt{3}y+\sqrt{5})(2x^2+3y^2+5-\sqrt{6}xy-\sqrt{5}y-\sqrt{10}x)$

$2\sqrt{2}{x}^3+3\sqrt{3}{y}^3+\sqrt{5}(5-3\sqrt{6}xy)=2\sqrt{2}{x}^3+3\sqrt{3}{y}^3+5\sqrt{5}-3\sqrt{6}\times \sqrt{5}xy$
$={\left(\sqrt{2}x\right)}^3+{\left(\sqrt{3}y\right)}^3+{\left(\sqrt{5}\right)}^3-3\times \sqrt{2}x\times \sqrt{3}y\times \sqrt{3}y$
$=(\sqrt{2}x+\sqrt{3}y+\sqrt{5})(2x^2+3y^2+5-\sqrt{6}xy-\sqrt{5}y-\sqrt{10}x)(\because a^3+b^3+c^3-3abc=(a+b+c\left)\right(a^2+b^2+c^2-ab-bc-ca\left)\right)$