The expression \((3a^2 + 2b^2)^2\) represents a binomial raised to the power of 2. We will expand this expression using the binomial expansion formula:

\[
(x + y)^2 = x^2 + 2xy + y^2
\]

Here, \(x = 3a^2\) and \(y = 2b^2\). Now let's expand:

\[
(3a^2 + 2b^2)^2 = (3a^2)^2 + 2(3a^2)(2b^2) + (2b^2)^2
\]

Step by step:

1. \((3a^2)^2 = 9a^4\)
2. \(2(3a^2)(2b^2) = 12a^2b^2\)
3. \((2b^2)^2 = 4b^4\)

Now, putting it all together:

\[
(3a^2 + 2b^2)^2 = 9a^4 + 12a^2b^2 + 4b^4
\]

This is the expanded form of the expression.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you expand \((2x^2 + 5y^2)^2\)?
2. Can you factor \(9a^4 + 12a^2b^2 + 4b^4\)?
3. What is the general form for expanding \((x + y)^3\)?
4. How does binomial expansion apply to higher powers?
5. Can binomial expansion be applied to non-polynomial expressions?

**Tip:** Always start by identifying \(x\) and \(y\) in binomial expressions before expanding.

Explore the binomial expansion of (3a^2 + 2b^2)^2 with a detailed step-by-step solution. Learn how to apply the binomial expansion formula and work through polynomial expressions. This problem is ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation