Armando used algebra tiles to represent the product \(3 \times (2x - 1)\).

Which is true regarding Armando's use of algebra tiles?

A. He used the algebra tiles correctly.
B. He did not represent the two original factors correctly.
C. The signs on some of the products are incorrect.
D. Some of the products do not show the correct powers of [tex]\(x\)[/tex].



Answer :

Let's analyze Armando's algebra tiles representation step-by-step to determine which statements about his work are true based on the given expression \(3 \times (2x - 1)\).

### Step-by-Step Solution:

1. Understanding the Expression:
- The expression Armando is working with is \(3 \times (2x - 1)\).
- This means he needs to distribute the 3 across the terms inside the parentheses:

[tex]\[ 3 \times (2x - 1) = 3 \times 2x + 3 \times (-1) \][/tex]

2. Distributing the 3:
- First, we multiply 3 by \(2x\):
[tex]\[ 3 \times 2x = 6x \][/tex]
- Second, we multiply 3 by \(-1\):
[tex]\[ 3 \times (-1) = -3 \][/tex]

3. Combining the Results:
- The simplified expression after distribution is:
[tex]\[ 6x - 3 \][/tex]

4. Analyzing Armando's Algebra Tiles:
- According to the distribution:
- Armando should have tiles representing \(6x\): six \(x\)-tiles.
- He should also have tiles representing \(-3\): three negative 1-tiles.

5. Verifying Armando's Representation:
- Armando's representation would be correct if:
- He used 6 \(x\)-tiles to represent \(6x\).
- He used three negative 1-tiles to represent \(-3\).
- He should have used the tiles correctly, representing each factor as \(6x - 3\).
- The signs of the products (positive and negative) should be accurate.
- All terms should reflect the correct powers of \(x\), which in this case, is simply \(x\).

### Conclusion:
Based on the analysis, we determine the following:
- Armando used the algebra tiles correctly.
- He represented the original factors (3 and \(2x - 1\)) correctly.
- The signs on the products (\(6x\) and \(-3\)) are correct.
- The powers of \(x\) are represented correctly (as just \(x\)).

Thus, the only true statement is:
- He used the algebra tiles correctly.

Therefore, the correct answer is:
- He used the algebra tiles correctly.