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To solve the trinomial in part **K**:  
\[
\frac{4}{9} x^2 - \frac{4}{3} x + x^2
\]

We need to simplify and factor it. Let's follow the steps:

### Step 1: Combine like terms
The expression is:
\[
\frac{4}{9} x^2 - \frac{4}{3} x + x^2
\]
Notice that there are two terms with \(x^2\). Combine them:
\[
\left(\frac{4}{9} + 1\right) x^2 - \frac{4}{3} x
\]
To combine \(\frac{4}{9} x^2\) and \(x^2\), rewrite \(x^2\) as \(\frac{9}{9} x^2\). This gives:
\[
\left(\frac{4}{9} + \frac{9}{9}\right) x^2 - \frac{4}{3} x
= \frac{13}{9} x^2 - \frac{4}{3} x
\]

### Step 2: Factor common terms
Now, we can factor out the greatest common factor (GCF). Notice that \(\frac{4}{3}x\) can be factored by taking out a common factor of \(x\) from both terms:
\[
x \left(\frac{13}{9}x - \frac{4}{3}\right)
\]

This is the factored form of the expression. 

Would you like a more detailed breakdown or further explanation? Here are some related questions to deepen your understanding:

1. How do we handle factoring when coefficients are fractions?
2. What techniques can be used to factor a trinomial when there are common terms?
3. Can we factor this trinomial in a different way?
4. What is the process of finding the greatest common factor in polynomials?
5. How do you simplify algebraic expressions with fractions?

**Tip**: Always check if you can simplify terms before attempting to factor complex expressions.

Learn how to factor the trinomial 4/9 x^2 - 4/3 x + x^2 step-by-step. This example covers algebraic concepts such as combining like terms and factoring out the greatest common factor (GCF). Suitable for students in Grades 8-10.

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