Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Did Cherise use algebra tiles to correctly represent the product of [tex][tex]$(x-2)(x-3)$[/tex][/tex]?

A. No, she did not multiply the [tex]x[/tex]-tiles by the negative integer tiles correctly.
B. No, she did not multiply the negative integer tiles by the other negative integer tiles correctly.
C. No, she did not add the terms together correctly.
D. Yes, the product is [tex][tex]$x^2 - 5x - 6$[/tex][/tex].

Sagot :

GinnyAnswer
Let's determine the product of [tex]\((x - 2)(x - 3)\)[/tex] step by step and see if Cherise's final result is [tex]\(x^2 - 5x - 6\)[/tex].

We can solve this by expanding the expression:

1. Distribute each term in the first binomial to each term in the second binomial:

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

2. Apply the distributive property (also known as the FOIL method) to each term:

- First, multiply [tex]\(x\)[/tex] by [tex]\(x\)[/tex] and then [tex]\(x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[ x \cdot x + x \cdot (-3) = x^2 - 3x \][/tex]

- Next, multiply [tex]\(-2\)[/tex] by [tex]\(x\)[/tex] and then [tex]\(-2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[ -2 \cdot x + (-2) \cdot (-3) = -2x + 6 \][/tex]

3. Combine all the terms together:

[tex]\[ x^2 - 3x - 2x + 6 \][/tex]

4. Simplify the expression by combining like terms (combine the [tex]\(x\)[/tex]-terms):

[tex]\[ x^2 - 3x - 2x + 6 = x^2 - 5x + 6 \][/tex]

Therefore, the correct product of [tex]\((x - 2)(x - 3)\)[/tex] is indeed [tex]\(x^2 - 5x + 6\)[/tex].

Now let's analyze Cherise's representation based on the possible mistakes:

1. Incorrect multiplication of the [tex]\(x\)[/tex]-tiles by the negative integer tiles: This means Cherise made an error in multiplying [tex]\(x\)[/tex] by [tex]\(-3\)[/tex] and/or [tex]\(-2\)[/tex] by [tex]\(x\)[/tex]. But our distribution indicates [tex]\(x \cdot (-3) = -3x\)[/tex] and [tex]\(-2 \cdot x = -2x\)[/tex] which are correct.

2. Incorrect multiplication of the negative integer tiles by the other negative integer tiles: This refers to a mistake in multiplying [tex]\(-2\)[/tex] by [tex]\(-3\)[/tex]. Our result shows [tex]\(-2 \cdot (-3) = 6\)[/tex], which is correct.

3. Incorrect addition of the terms together: Cherise might have made a mistake in combining the terms. Combining [tex]\(-3x\)[/tex] and [tex]\(-2x\)[/tex] correctly gives [tex]\(-5x\)[/tex]. However, if she incorrectly added these terms, she could have gotten the wrong middle term.

4. Correct representation: Her final result is indeed [tex]\(x^2 - 5x + 6\)[/tex], which matches our derived product.

Based on the given result and our calculations, we conclude:

Yes, the product is [tex]\(x^2 - 5x + 6\)[/tex].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.