Question

Factorise the following trinomials:
$\frac{x^2}{4y^2}-\frac{1}{3}+\frac{y^2}{9x^2}$

Answer 1

$\frac{x^2}{4y^2}+\frac{y^2}{9x^2}-\frac{1}{3}$

$={\left(\frac{x}{2y}\right)}^2+{\left(\frac{y}{3x}\right)}^2-\frac{1}{3}$

Add and Subtract $2\times \frac{x}{2y}\times \frac{y}{3x}$ we get

$={\left(\frac{x}{2y}\right)}^2+{\left(\frac{y}{3x}\right)}^2-2\times \frac{x}{2y}\times \frac{y}{3x}+2\times \frac{x}{2y}\times \frac{y}{3x}-\frac{1}{3}$

$={(\frac{x}{2y}-\frac{y}{3x})}^2+2\times \frac{x}{2y}\times \frac{y}{3x}-\frac{1}{3}$

$={(\frac{x}{2y}-\frac{y}{3x})}^2+\frac{1}{3}-\frac{1}{3}$

$={(\frac{x}{2y}-\frac{y}{3x})}^2$