2. Polynomials
easy

Factorise : $\frac{25}{4} x^{2}-\frac{y^{2}}{9}$

Option A
Option B
Option C
Option D

Solution

we have   $\frac{25}{4} x^{2}-\frac{y^{2}}{9}=\left(\frac{5}{2} x\right)^{2}-\left(\frac{y}{3}\right)^{2}$

Now comparing it with Identity $III$, we get

$\frac{25}{4} x^{2}-\frac{y^{2}}{9}=\left(\frac{5}{2} x\right)^{2}-\left(\frac{y}{3}\right)^{2}$

$=\left(\frac{5}{2} x+\frac{y}{3}\right)\left(\frac{5}{2} x-\frac{y}{3}\right)$

Standard 9
Mathematics

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