The function given is \( f(x) = (6x + 5)^2 \).

To expand this, apply the formula \( (a + b)^2 = a^2 + 2ab + b^2 \).

Let \( a = 6x \) and \( b = 5 \), so:

\[
f(x) = (6x + 5)^2 = (6x)^2 + 2(6x)(5) + (5)^2
\]
Now, calculate each term:

\[
(6x)^2 = 36x^2, \quad 2(6x)(5) = 60x, \quad (5)^2 = 25
\]

So, the expanded form of \( f(x) \) is:

\[
f(x) = 36x^2 + 60x + 25
\]

Would you like further details on how this was done or have any questions?

Here are five related questions:
1. What is the derivative of \( f(x) = (6x + 5)^2 \)?
2. How would you find the roots of \( f(x) = 36x^2 + 60x + 25 \)?
3. What is the vertex of the quadratic function \( f(x) = 36x^2 + 60x + 25 \)?
4. How would you factor the expanded form \( f(x) = 36x^2 + 60x + 25 \)?
5. How can you graph \( f(x) = (6x + 5)^2 \)?

**Tip**: Always check if a quadratic function can be factored or simplified after expansion to make solving easier.

Learn how to expand and simplify the expression (6x + 5)^2 using the binomial expansion formula. This step-by-step solution explains each part of the process, from applying the expansion formula to calculating individual terms. Ideal for students in Grades 9-11.

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