To solve the expression \((6p + 3)(9p - 3)\), we can expand it using the distributive property (also known as the FOIL method for binomials):

\[
(6p + 3)(9p - 3)
\]

First, distribute \(6p\) to both terms in the second binomial:

\[
6p \times 9p + 6p \times (-3) = 54p^2 - 18p
\]

Next, distribute \(3\) to both terms in the second binomial:

\[
3 \times 9p + 3 \times (-3) = 27p - 9
\]

Now, combine all these terms:

\[
54p^2 - 18p + 27p - 9
\]

Combine the like terms \(-18p\) and \(27p\):

\[
54p^2 + 9p - 9
\]

The expression simplifies to:

\[
\boxed{54p^2 + 9p - 9}
\]

This is the expanded form of the expression. If you have a specific value of \(p\) you'd like to solve for, plug it in and calculate.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you factor the expression \(54p^2 + 9p - 9\)?
2. If \(p = 1\), what is the value of the expression?
3. How does expanding binomials relate to the distributive property?
4. What is the general process to solve quadratic equations like \(54p^2 + 9p - 9 = 0\)?
5. Can the expression be simplified further using the greatest common factor (GCF)?

**Tip:** Always check for common factors before expanding or simplifying expressions, as it can make the process easier.

Learn how to expand and simplify the expression (6p + 3)(9p - 3) using the distributive property and combine like terms. This detailed solution covers key algebraic concepts and formulas, including the FOIL method and quadratic equations. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation