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

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].

Sagot :

GinnyAnswer
Let's solve the given problem step-by-step:

We have the expression [tex]\(3 \times (2x - 1)\)[/tex]. To find the product, we need to distribute the [tex]\(3\)[/tex] across the terms inside the parentheses. Here's the detailed step-by-step process:

1. Start with the given factors: [tex]\(3\)[/tex] and [tex]\((2x - 1)\)[/tex].

2. Distribute the [tex]\(3\)[/tex] to each term inside the parentheses:
[tex]\[ 3 \times (2x - 1) = 3 \times 2x + 3 \times (-1) \][/tex]

3. Multiply each term individually:
[tex]\[ 3 \times 2x = 6x \][/tex]
[tex]\[ 3 \times (-1) = -3 \][/tex]

4. Combine the results:
[tex]\[ 3 \times (2x - 1) = 6x - 3 \][/tex]

So, the product is [tex]\(6x - 3\)[/tex].

Now, let's consider the options regarding Armando's use of algebra tiles:

1. He used the algebra tiles correctly:
If Armando's algebra tiles represented [tex]\(3\)[/tex] groups of [tex]\(2x - 1\)[/tex] and combined them to show [tex]\(6x - 3\)[/tex], then he used the tiles correctly.

2. He did not represent the two original factors correctly:
If Armando's initial setup with algebra tiles did not correctly feature [tex]\(3\)[/tex] and [tex]\((2x - 1)\)[/tex] in appropriate quantities, then this statement would be true. However, based on the correct product of [tex]\(6x - 3\)[/tex], this seems unlikely.

3. The signs on some of the products are incorrect:
If Armando's tiles showed incorrect signs (for example, representing [tex]\(2x - 1\)[/tex] as [tex]\(2x + 1\)[/tex]), the final product wouldn't match [tex]\(6x - 3\)[/tex]. But since the correct product is given, this statement would be false.

4. Some of the products do not show the correct powers of [tex]\(x\)[/tex]:
The problem only involves the first power of [tex]\(x\)[/tex]; if Armando’s product was correct, then all powers (in this case, just [tex]\(x\)[/tex]) would be shown correctly.

Since the product [tex]\(6x - 3\)[/tex] matches our expanded expression exactly, we can conclude that Armando used the algebra tiles correctly. Hence, the true statement regarding Armando's use of algebra tiles is:

- He used the algebra tiles correctly.
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