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

1 Answer
Jim G.
May 2, 2017

#-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)#

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