Did Cherise use algebra tiles to correctly represent the product of (x – 2)(x – 3)?
A. No, she did not multiply the x-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 x2 – 5x – 6.
The Correct Answer and Explanation is:
The correct answer is A. No, she did not multiply the x-tiles by the negative integer tiles correctly.
Explanation:
To solve the expression ((x – 2)(x – 3)) using algebra tiles, we can break the expression down step by step. Let’s first expand the product of the two binomials using the distributive property (also known as FOIL):
[
(x – 2)(x – 3) = x(x – 3) – 2(x – 3)
]
Now, applying the distributive property:
[
x(x – 3) = x^2 – 3x
]
[
-2(x – 3) = -2x + 6
]
Thus, the expanded form of the product is:
[
x^2 – 3x – 2x + 6
]
Simplifying the terms involving (x):
[
x^2 – 5x + 6
]
Therefore, the product of ((x – 2)(x – 3)) is (x^2 – 5x + 6).
Addressing the Answer Choices:
A. No, she did not multiply the x-tiles by the negative integer tiles correctly.
- This choice suggests a mistake in how the x-tiles were multiplied by the negative integer tiles. When using algebra tiles to represent the expression, we expect the negative integer tiles to be correctly multiplied by the (x)-tiles. A common error would be failing to correctly pair the tiles or missing the signs in the multiplication process. This is a plausible explanation of why Cherise’s representation might be incorrect.
B. No, she did not multiply the negative integer tiles by the other negative integer tiles correctly.
- This choice would be incorrect because when multiplying the binomials, the multiplication between the negative integers (-2) and (-3) should result in a positive (+6). The issue here is more likely with the interaction between (x)-tiles and integer tiles, not the multiplication of the negative integers themselves.
C. No, she did not add the terms together correctly.
- While adding terms incorrectly could be a mistake in simplification, this is not the primary concern with algebra tiles. The focus in this problem is more likely on the multiplication process rather than the final addition.
D. Yes, the product is (x^2 – 5x – 6).
- This option is incorrect because the correct product is (x^2 – 5x + 6), not (x^2 – 5x – 6). The sign of the constant term should be positive, as shown in the correct expansion.
Thus, Answer A is the best explanation of the error in Cherise’s use of algebra tiles.