Question

How do you factor `9-(k+3)^2`?

Answer 1

`-k(6+k)`

Explanation:

This expression is a `color(blue)"difference of squares"` which factorises in general as.

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^2-b^2=(a-b)(a+b))color(white)(2/2)|)))`

`"for " 9-(k+3)^2`

`a=3" and " b=k+3`

`rArr9-(k+3)^2=(3-(k+3))(3+(k+3))`

`color(white)(rArr9-(k+3)^2)=(3-k-3)(6+k)`

`color(white)(rArr9-(k+3)^2)=-k(6+k)`