Factorise: frac{25}{4} x^{2}-frac{y^{2}}{9} | vedclass

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Question

(A) We have the expression: $\frac{25}{4} x^{2}-\frac{y^{2}}{9}$This can be written as: $\left(\frac{5}{2} x\right)^{2}-\left(\frac{y}{3}\right)^{2}$U

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We have the expression: $\frac{25}{4} x^{2}-\frac{y^{2}}{9}$This can be written as: $\left(\frac{5}{2} x\right)^{2}-\left(\frac{y}{3}\right)^{2}$Using the algebraic identity $a^{2}-b^{2} = (a+b)(a-b)$,where $a = \frac{5}{2} x$ and $b = \frac{y}{3}$,we get:$\frac{25}{4} x^{2}-\frac{y^{2}}{9} = \left(\frac{5}{2} x+\frac{y}{3}\right)\left(\frac{5}{2} x-\frac{y}{3}\right)$

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

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