Question

How do you factor `64-y^2`?

Answer 1

Here's the result: `(8-y)(8+y)`

Explanation:

Start off by appreciating the fact that: `(a-b)(a+b)=a^2+color(red)(ab-ab)-b^2`
`=>(a-b)(a+b)= a^2-b^2`

So, generally `a^2-b^2 = (sqrt(a^2)-sqrt(b^2))(sqrt(a^2)+sqrt(b^2))`

Therefore, in our present situation,
`(64-y^2)` by comparing with the above results,
`64-y^2= = (sqrt(64)-sqrt(y^2))(sqrt(64)+sqrt(y^2))=(8-y)(8+y)`

That's it!