\sf\large\green{\underbrace{\red{Question*}}}: Factorize 4 {a}^(2) - \frac{ {y}^(2) }{16} ​

Question

`\sf\large\green{\underbrace{\red{Question*}}}:`

Factorize

`4 {a}^(2) - \frac{ {y}^(2) }{16}`
​

Answer 1

(2a -
`(y)/(4)` )(2a +
`(y)/(4)` )

Explanation:

4a² -
`(y^2)/(16)` ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4a² -
`(y^2)/(16)`

= (2a)² - (
`(y)/(4)` )²

= (2a -
`(y)/(4)` )(2a +
`(y)/(4)` )