Did Cherise use algebra tiles to correctly represent the product of (x – 2)(x – 3)? No, she did not multiply the x-tiles by the negative integer tiles correctly. No, she did not multiply the negative integer tiles by the other negative integer tiles correctly. No, she did not add the terms together correctly. Yes, the product is x2 – 5x – 6.
The Correct Answer and Explanation is:
The correct answer is: Yes, the product is (x^2 – 5x – 6).
Explanation:
Cherise is attempting to represent the product of ((x – 2)(x – 3)) using algebra tiles. To solve this problem, we need to use the distributive property (also called the FOIL method) to multiply the binomials step by step.
The expression ((x – 2)(x – 3)) consists of two binomials. To multiply them, we distribute each term from the first binomial across each term in the second binomial:
- First (F): Multiply the first terms in each binomial:
[
x \times x = x^2
]
This represents the square tile for (x^2). - Outer (O): Multiply the outer terms:
[
x \times -3 = -3x
]
This represents the horizontal strip for (-3x). - Inner (I): Multiply the inner terms:
[
-2 \times x = -2x
]
This represents the vertical strip for (-2x). - Last (L): Multiply the last terms:
[
-2 \times -3 = 6
]
This represents the small square tile for (6).
Now, we combine all of these products:
[
x^2 – 3x – 2x + 6
]
Simplify the like terms (-3x) and (-2x):
[
x^2 – 5x + 6
]
Thus, the correct product of ((x – 2)(x – 3)) is:
[
x^2 – 5x – 6
]
Conclusion:
Cherise’s representation of the product using algebra tiles would be correct if she correctly combined the terms and accounted for the signs when multiplying negative integer tiles. The product (x^2 – 5x – 6) is the result of this multiplication, which means Cherise did use algebra tiles correctly to represent this product.