Question

$9x {}^{2} + \frac{9}{25y {}^{2} } - \frac{18x}{5y}$
$(a + b) { {}^{2} }^{} = a {}^{2} + 2ab + b {}^{2}$

Answer 1

hello friend
$= 9 {x}^{2} + \frac{9}{25 {y}^{2} } - \frac{18x}{5y} \\ = {(3x)}^{2} + \frac{ {3}^{2} }{ {(5y)}^{2} } - 2(3x)( \frac{3}{5y} ) \\ = {(3x + \frac{3}{5y}) }^{2}$

Answer 2

Solution :

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Given :

To factorize : $9x^2 + \frac{9}{25y^2} - \frac{18x}{5y}$

Using the identity,

(a + b)² = a² + 2ab + b²

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This identity is more suitable for the given equation,

⇒ (a - b)² = a² + 2ab + b²

anyway,

As per you request,

I use (a + b)² identity,.

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To factorize by using an identity, we need to bring the equation (or polynomial) to the LHS (or) RHS part of the identity,.

⇒ $9x^2 + \frac{9}{25y^2} - \frac{18x}{5y}$

⇒ $(3x)^2 + (\frac{3}{5y})^2 - 2(3)(\frac{(3x)}{5y})$

⇒ It is in the form a² + 2ab + b²

where,

a = 3x,

b = - $\frac{3}{5y}$

⇒ $(3x + (- \frac{3}{5y}))^2$

⇒ $(3x - \frac{3}{5y} )^2$

∴ $9x^2 + \frac{9}{25y^2} - \frac{18x}{5y}$ = $(3x - \frac{3}{5y} )^2$

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                                        Hope it Helps !!