Answer:
ƒ(a + h) = 2(a^3 + 3a^2h + 3ah^2 + h^3)
Step-by-step explanation:
Put (a+h) in place of x and "simplify" the expression.
f(x) = 2x^3
f(a +h) = 2(a +h)^3 = 2(a^3 +3a^2h +3ah^2 +h^3) . . . . matches 1st choice
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It helps to know the expansion of a binomial:
(a +b)^3 = a^3 +3a^2b +3ab^2 +b^3
Even if you don't, you can multiply it out.
(a +b)^3 = (a +b)(a^2 +2ab +b^2) = a^3 +2a^2b +ab^2 +a^2b +2ab^2 +b^3
= a^3 +3a^2b +3ab^2 +b^3
