Given the function \( f(b) = (b + 6)(b - 2) \), you can expand it to find a simplified expression.

Let's expand it:

\[
f(b) = (b + 6)(b - 2)
\]

Use the distributive property (also known as the FOIL method for binomials):

\[
f(b) = b \cdot b + b \cdot (-2) + 6 \cdot b + 6 \cdot (-2)
\]

Simplifying each term:

\[
f(b) = b^2 - 2b + 6b - 12
\]

Combine like terms:

\[
f(b) = b^2 + 4b - 12
\]

So, the simplified form of the function is:

\[
f(b) = b^2 + 4b - 12
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do you factorize a quadratic expression?
2. What is the vertex form of a quadratic function?
3. How do you find the roots of \( f(b) = b^2 + 4b - 12 \)?
4. What is the significance of the discriminant in a quadratic equation?
5. How does the graph of \( f(b) = b^2 + 4b - 12 \) look?

**Tip:** When dealing with quadratic functions, always try to simplify the expression first to make further calculations easier.

Explore how to expand and simplify the quadratic expression (b+6)(b-2) using the distributive property. This step-by-step solution guides you through polynomial expansion, resulting in a simplified quadratic form b^2 + 4b - 12. Ideal for students in Grades 8-10.

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