How do you simplify #\frac { 1- ( x + h ) ^ { 3} - ( 1- x ^ { 3} ) } { h }#?

1 Answer
May 31, 2018

#-3x^2-3hx+h^2#

Explanation:

#"using the expansion for "(x+h)^3#

#•color(white)(x)(x+h)^3=x^3+3x^2h+3xh^2+h^3#

#=(1-(x^3+3x^2h+3xh^2+h^3)-(1-x^3))/h#

#=(cancel(1)cancel(-x^3)-3x^2h-3xh^2-h^3cancel(-1)cancel(+x^3))/h#

#=(-cancel(h)(3x^2+3xh+h^2))/cancel(h)#

#=-3x^2-3hx-h^2#