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First find the expression for f(a+h)
f(x) = x^2 - 3
f(x) = (x)^2 - 3
f(a+h) = (a+h)^2 - 3 ... replace every x with a+h
f(a+h) = a^2+2ah+h^2 - 3 ... expand out (a+h)^2.
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Then do the same for f(a)
f(x) = x^2 - 3
f(a) = a^2 - 3 ... replace every x with 'a'
I'm marking it in red so we can use it later
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Now that we know f(a+h) and f(a), we simply subtract
f(a+h) - f(a) = [ f(a+h) ] - [ f(a) ]
f(a+h) - f(a) = [ a^2+2ah+h^2 - 3 ] - [ a^2-3 ]
f(a+h) - f(a) = a^2+2ah+h^2 - 3 - a^2 + 3
f(a+h) - f(a) = 2ah+h^2
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Final Answer: 2ah+h^2
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