Question

Determine ƒ(a + h) for ƒ(x) = 2x3.

ƒ(a + h) = 2(a3 + 3a2h + 3ah2 + h3)

ƒ(a + h) = 8(a3 + 3a2h + 3ah2 + h3)

ƒ(a + h) = 8(a3 + h3)

ƒ(a + h) = 2(a3 + a2h + ah2 + h3)

Answer 1

ƒ(a + h) = 2(a^3 + 3a^2h + 3ah^2 + h^3)

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