Question
Two students in Ms. Chau's class were asked to write an equivalent expression for the expression (a−6)(a−4)
. Identify the student with the correct work and where the mistakes were in the other student's work.
(1 point)
Responses
Gabrielle is correct; Brittany did not use arrows to show the distributive property before she multiplied.
Gabrielle is correct; Brittany did not use arrows to show the distributive property before she multiplied.
Brittany is correct; Gabrielle multiplied the constants −6⋅−4
and got −24
, and she should have gotten +24
.
Brittany is correct; Gabrielle multiplied the constants negative 6 times negative 4 and got negative 24, and she should have gotten plus 24.
Brittany is correct; Gabrielle used arrows to show the distributive property.
Brittany is correct; Gabrielle used arrows to show the distributive property.
Gabrielle is correct; Brittany multiplied the constants −6⋅−4
and got +24
, and she should have gotten −24
.
Gabrielle is correct; Brittany multiplied the constants negative 6 times negative 4 and got plus 24, and she should have gotten negative 24.
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. Identify the student with the correct work and where the mistakes were in the other student's work.
(1 point)
Responses
Gabrielle is correct; Brittany did not use arrows to show the distributive property before she multiplied.
Gabrielle is correct; Brittany did not use arrows to show the distributive property before she multiplied.
Brittany is correct; Gabrielle multiplied the constants −6⋅−4
and got −24
, and she should have gotten +24
.
Brittany is correct; Gabrielle multiplied the constants negative 6 times negative 4 and got negative 24, and she should have gotten plus 24.
Brittany is correct; Gabrielle used arrows to show the distributive property.
Brittany is correct; Gabrielle used arrows to show the distributive property.
Gabrielle is correct; Brittany multiplied the constants −6⋅−4
and got +24
, and she should have gotten −24
.
Gabrielle is correct; Brittany multiplied the constants negative 6 times negative 4 and got plus 24, and she should have gotten negative 24.
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve for the equivalent expression for \((a−6)(a−4)\), we need to apply the distributive property (also known as the FOIL method for binomials):
\[
(a−6)(a−4) = a \cdot a + a \cdot (-4) + (-6) \cdot a + (-6) \cdot (-4)
\]
Calculating each term:
1. \(a \cdot a = a^2\)
2. \(a \cdot (-4) = -4a\)
3. \((-6) \cdot a = -6a\)
4. \((-6) \cdot (-4) = 24\)
Combining these results, we get:
\[
a^2 - 4a - 6a + 24 = a^2 - 10a + 24
\]
Now, let's analyze the responses:
- Gabrielle is correct in the multiplication of constants; \((-6) \cdot (-4) = 24\).
- Brittany could have gotten \(-24\) if she made a mistake in that multiplication.
Given these statements:
1. **Gabrielle is correct; Brittany made an error in multiplying the constants \(-6\) and \(-4\), possibly getting \(-24\) instead of \(+24\).**
2. **Brittany is incorrect; Gabrielle’s result of \(+24\) is accurate.**
Thus, the correct response to identify the students' work is:
**Gabrielle is correct; Brittany multiplied the constants −6⋅−4 and got −24, and she should have gotten +24.**
\[
(a−6)(a−4) = a \cdot a + a \cdot (-4) + (-6) \cdot a + (-6) \cdot (-4)
\]
Calculating each term:
1. \(a \cdot a = a^2\)
2. \(a \cdot (-4) = -4a\)
3. \((-6) \cdot a = -6a\)
4. \((-6) \cdot (-4) = 24\)
Combining these results, we get:
\[
a^2 - 4a - 6a + 24 = a^2 - 10a + 24
\]
Now, let's analyze the responses:
- Gabrielle is correct in the multiplication of constants; \((-6) \cdot (-4) = 24\).
- Brittany could have gotten \(-24\) if she made a mistake in that multiplication.
Given these statements:
1. **Gabrielle is correct; Brittany made an error in multiplying the constants \(-6\) and \(-4\), possibly getting \(-24\) instead of \(+24\).**
2. **Brittany is incorrect; Gabrielle’s result of \(+24\) is accurate.**
Thus, the correct response to identify the students' work is:
**Gabrielle is correct; Brittany multiplied the constants −6⋅−4 and got −24, and she should have gotten +24.**
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