Simplify expression

I don't understand it how it solved. Can you please do it in a different way.
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mustish1Asked:
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sdstuberConnect With a Mentor Commented:
it's just substitution.  There's really no trick or other method to it. In the example they skipped some of the trivial arithmetic; but we can show all of it.

f(4+h) - f(4)

solve it in two parts

part1: f(4+h) and then part2: f(4)  when you have both, subtract part 2 from part 1

part1:  x= 4+h

so  f(x) = x^2 - 2 = (4+h)^2 - 2 = 4^2 + 8h + h^2 - 2 = 16 + 8h + h^2 -2 = h^2 + 8h +14

part2: x = 4

f(x) = x^2 - 2 = 4^2 - 2 = 16 -2 = 14


f(4+h) - f(4) =    (h^2 + 8h + 14) -  (14) = h^2 + 8h
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aburrConnect With a Mentor Commented:
What is f(x)?
f(x) = x^2 -2
What if x = 4 +h?      what is f(x) then?   It is
f(4+h) = (4+h)^2 -2
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What if x= 4   What is f(x) then?    It is
f(4) = 4^2 = 16- 2 = 14   so

(4+h)^2 -2 = 14    do the square

16 + 8h + h^2 – 2 = 14          simplify

h^2 + 8h
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mustish1Author Commented:
Thank You.
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