To simplify \((3x + 1)^2\), you need to expand the square:

\[
(3x + 1)^2 = (3x + 1)(3x + 1)
\]

Now, apply the distributive property (FOIL method):

\[
= 3x(3x) + 3x(1) + 1(3x) + 1(1)
\]

Simplifying each term:

\[
= 9x^2 + 3x + 3x + 1
\]

Combine like terms:

\[
= 9x^2 + 6x + 1
\]

So, \((3x + 1)^2 = 9x^2 + 6x + 1\).

Would you like any further details or clarification?

Here are 5 related questions:
1. What is the square of \((2x - 5)\)?
2. How do you expand \((4x + 2)^2\)?
3. How do you factor \(9x^2 + 6x + 1\)?
4. What is the difference between squaring a binomial and a trinomial?
5. What is the general formula for \((a + b)^2\)?

**Tip**: Always combine like terms when expanding expressions to simplify the result.

Learn how to expand and simplify the expression (3x + 1)² step-by-step. This problem covers important algebraic concepts like binomial expansion and the distributive property. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation