Question

(25/4x^2-1/9y^2) factorise it

Answer 1

$\Big(\frac{25}{4x^{2}} - \frac{1}{9y^{2}}\Big)$

$= \Big(\frac{5}{2x}\Big)^{2} - \Big(\frac{1}{3y}\Big)^2$

$= \Big( \frac{5}{2x} + \frac{1}{3y}\Big)\Big( \frac{5}{2x} - \frac{1}{3y}\Big)$

/* By Algebraic Identity */

$\boxed { \pink { a^{2} - b^{2} = (a+b)(a-b) }}$

Therefore.,

$\red{\Big(\frac{25}{4x^{2}} - \frac{1}{9y^{2}}\Big)}$

$\green { = \Big( \frac{5}{2x} + \frac{1}{3y}\Big)\Big( \frac{5}{2x} - \frac{1}{3y}\Big)}$

•••♪

Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Equation : }}}$

$\:\:$

• ${\Big(\dfrac{25}{{4x}^{2}} - \dfrac{1}{{9y}^{2}}\Big)}$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: To \: Find : }}}$

$\:\:$

• Factorise equation

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Some \: information : }}}$

$\:\:$

• $\footnotesize{\ {a}^}2} - {b}^{2} = ( a + b )( a - b )}$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Solution :}}}$

$\:\:$

${\Big(\dfrac{25}{{4x}^{2}} - \dfrac{1}{{9y}^{2}}\Big)}$

${ = {\Big(\dfrac{5}{2x}\Big)}^{2} - {\Big(\dfrac{1}{3y}\Big)}^{2}}$

${= \Big(\dfrac{5}{2x} + \dfrac{1}{3y}\Big) \Big(\dfrac{5}{2x} - \dfrac{1}{3y}\Big)}$

$\:\:$

$\bold{Answer = \Big(\dfrac{5}{2x} + \dfrac{1}{3y}\Big) \Big(\dfrac{5}{2x} - \dfrac{1}{3y}\Big)}$