Question : What is the value of $\frac{4x^2+9y^2+12xy}{144}$?
Option 1: $(\frac{x}{3} + \frac{y}{4})^2$
Option 2: $(\frac{x}{3} + y)^2$
Option 3: $(\frac{x}{4} + \frac{y}{6})^2$
Option 4: $(\frac{x}{6} + \frac{y}{4})^2$
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Correct Answer: $(\frac{x}{6} + \frac{y}{4})^2$
Solution :
$\frac{4x^2+9y^2+12xy}{144}$
= $\frac{x^2}{36} +\frac{y^2}{16}+\frac{xy}{12}$
= $\frac{x^2}{36} +\frac{y^2}{16}+2×\frac{x}{6}×\frac{y}{4}$
= $(\frac{x}{6} + \frac{y}{4})^2$
Hence, the correct answer is $(\frac{x}{6} + \frac{y}{4})^2$.
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