Question

How to Factorize `256-x^2-2xy-y^2`?

Answer 1

`256-x^2-2xy-y^2 = (16-x-y)(16+x+y)`

Explanation:

The difference of squares identity can be written:

`A^2-B^2 = (A-B)(A+B)`

Use this with `A=16` and `B=(x+y)` as follows:

`256-x^2-2xy-y^2 = 16^2-(x^2+2xy+y^2)`

`color(white)(256-x^2-2xy-y^2) = 16^2-(x+y)^2`

`color(white)(256-x^2-2xy-y^2) = (16-(x+y))(16+(x+y))`

`color(white)(256-x^2-2xy-y^2) = (16-x-y)(16+x+y)`