Question 642640

Given: {{{f(x) = x^2 + 2x + 1}}}, find {{{f(x + h)}}} and simplify

replace {{{x}}} with {{{x+h}}}:


{{{f(x+h) = (x+h)^2 + 2(x+h) + 1}}}


{{{f(x+h) = (x+h)(x+h) + 2(x+h) + 1}}}....replace {{{2(x+h)}}} with {{{(x+h)+(x+h)}}}



{{{f(x+h) = (x+h)(x+h) +(x+h) +(x+h)+ 1}}}...group first two and second two terms together

{{{f(x+h) = ((x+h)(x+h) +(x+h)) +((x+h)+ 1)}}}

{{{f(x+h) = (x+h)((x+h) +1) +((x+h)+ 1)}}}

{{{f(x+h) = ((x+h)+1)((x+h)+ 1)}}}

{{{f(x+h) = (x+h+1)(x+h+ 1)}}}