Question

Factories completely %20%7D%20%20-%20%20%5Cfrac%7B1%7D%7B9%7D%20" id="TexFormula1" title=" \frac{x {2}^{} }{4y {}^{2 } } - \frac{1}{9} " alt=" \frac{x {2}^{} }{4y {}^{2 } } - \frac{1}{9} " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

see explanation

Step-by-step explanation:

This is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

$\frac{x^2}{4y^2}$ = ( $\frac{x}{2y}$ )² ⇒ a = $\frac{x}{2y}$

$\frac{1}{9}$ = ( $\frac{1}{3}$ )² ⇒ b = $\frac{1}{3}$

Hence

$\frac{x^2}{4y^2}$ - $\frac{1}{9}$

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

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

Answer 2

Answer:

(x/2y + 1/3)(x/2y - 1/3).

Step-by-step explanation:

x^2/4y^2 - 1/9.

This is the difference of 2 squares:

The square root of x^2/4y^2 = x / 2y and square root of 1/9 is 1/3.

So we have:

x^2/4y^2 - 1/9

= (x/2y + 1/3)(x/2y - 1/3).