Question

State True or False.

$24\sqrt{3}{x}^3-125y^3=$$(2\sqrt{3}x-5y)(12x^2+10\sqrt{3}xy+25y^2)$

• A. True
• B. False

Answer 1

The correct option is A True

Formula used:$(x^3-y^3)=(x-y)(x^2+xy+y^2)$
$24\sqrt{3}{x}^3-125y^3=(2\sqrt{3}x{)}^3-(5y{)}^3$
$=(2\sqrt{3}x-5y)\left[\right(2\sqrt{3}x{)}^2+\left(2\sqrt{3}x\right)\left(5y\right)+\left(5y{)}^2\right]$
$=(2\sqrt{3}x-5y)(12x^2+10\sqrt{3}xy+25y^2)$