To expand the expression \((6a-5)(6a+6)\), we use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):

\[
(6a-5)(6a+6) = (6a)(6a) + (6a)(6) + (-5)(6a) + (-5)(6)
\]

Now, we compute each term:

1. **First:** \((6a)(6a) = 36a^2\)
2. **Outer:** \((6a)(6) = 36a\)
3. **Inner:** \((-5)(6a) = -30a\)
4. **Last:** \((-5)(6) = -30\)

Combining these results gives:

\[
36a^2 + 36a - 30a - 30
\]

Now, simplify by combining like terms:

\[
36a^2 + 6a - 30
\]

Thus, the expanded form of \((6a-5)(6a+6)\) is:

\[
36a^2 + 6a - 30
\]

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. How do you factor quadratic expressions like \(36a^2 + 6a - 30\)?
2. What is the FOIL method, and how does it apply to binomial multiplication?
3. How would

Learn how to expand the binomial expression (6a-5)(6a+6) using the FOIL method. This step-by-step solution breaks down the algebraic process and simplifies the result to 36a^2 + 6a - 30. Ideal for students in Grades 8-10 looking to strengthen their understanding of binomial expansion and algebraic techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation