Question

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

• A. $(\frac{x}{4}+\frac{y}{2})(\frac{x}{3}+\frac{y^2}{2})$
• B. $(\frac{x}{9}+\frac{y^2}{2})(\frac{x}{3}-\frac{y^2}{2})$
• C. $(\frac{x}{3}+\frac{y}{2})(\frac{x}{3}-\frac{y^2}{2})$
• D. None of these

Answer 1

Answer: (D)

None of these

$\frac{x^2}{9}+\frac{x{y}^2}{3}+\frac{y^4}{4}={\left(\frac{x}{3}\right)}^2+2\times \frac{x}{3}\times \frac{y^2}{2}+{\left(\frac{y^2}{2}\right)}^2={(\frac{x}{3}+\frac{y^2}{2})}^2=(\frac{x}{3}+\frac{y^2}{2})(\frac{x}{3}+\frac{y^2}{2})$