How do you simplify #\frac { 1- ( x + h ) ^ { 3} - ( 1- x ^ { 3} ) } { h }#?
1 Answer
May 31, 2018
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#