The function \( f(x) = (x+3)^3 \) is a cubic function. To expand it, we can apply the binomial expansion formula. Let's expand this step by step:

\[
f(x) = (x+3)^3
\]

Using the binomial expansion:

\[
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
\]

Here, \( a = x \) and \( b = 3 \):

\[
f(x) = x^3 + 3(x^2)(3) + 3(x)(3^2) + 3^3
\]

Simplifying:

\[
f(x) = x^3 + 9x^2 + 27x + 27
\]

Thus, the expanded form of \( f(x) = (x+3)^3 \) is:

\[
f(x) = x^3 + 9x^2 + 27x + 27
\]

Would you like to explore more details or ask any questions?

Here are five related questions:
1. What is the derivative of \( f(x) = (x+3)^3 \)?
2. How do you find the critical points of a cubic function?
3. Can you factor a cubic function like \( f(x) = (x+3)^3 \)?
4. What does the graph of \( f(x) = (x+3)^3 \) look like?
5. How do you solve \( (x+3)^3 = 0 \)?

**Tip**: For cubic functions, always look at both the expanded form and factored form when analyzing behavior, such as roots and critical points.

Explore the step-by-step expansion of the cubic function f(x) = (x+3)³ using the binomial expansion. Learn key algebraic concepts, formulas, and theorems related to cubic functions, suitable for students in Grades 10-12.

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