Question

How do you factor `40-(2y-w)^2`?

Answer 1

`(2sqrt10-2y+w)(2sqrt10+2y-w)`

Explanation:

`"factorise using the method of "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"note that " (2sqrt10)^2=40`

`rArr40-(2y-w)^2`

`=(2sqrt10)^2-(2y-w)^2`

`"with "a=2sqrt10" and "b=2y-w`

`(2sqrt10-(2y-w))(2sqrt10+(2y-w)`

`=(2sqrt10-2y+w)(2sqrt10+2y-w)`