Question

Factories completely

`\frac{x {2}^{} }{4y {}^(2 ) } - (1)/(9)`
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Answer 1

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

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).

Answer 2

see explanation

Explanation:

This is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

`(x^2)/(4y^2)` = (
`(x)/(2y)` )² ⇒ a =
`(x)/(2y)`

`(1)/(9)` = (
`(1)/(3)` )² ⇒ b =
`(1)/(3)`

Hence

`(x^2)/(4y^2)` -
`(1)/(9)`

= (
`(x)/(2y)` )² - (
`(1)/(3)` )²

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