Question
Which statements are true about the expression 8 (a + 7)? Check all that apply.
To simplify, distribute a to 8 and to 7.
8(a) can be rewritten as 8a.
8 (a + 7) can be rewritten as 8 (a) + 8 (7).
8 (a + 7) can be rewritten as 8 (a) + (7).
An equivalent expression is 15a.
An equivalent expression is 8 a + 7
An equivalent expression is 8 a + 56
To simplify, distribute a to 8 and to 7.
8(a) can be rewritten as 8a.
8 (a + 7) can be rewritten as 8 (a) + 8 (7).
8 (a + 7) can be rewritten as 8 (a) + (7).
An equivalent expression is 15a.
An equivalent expression is 8 a + 7
An equivalent expression is 8 a + 56
Answers
GPT-4o mini
Let's analyze the expression \(8(a + 7)\) and determine which statements are true.
1. **To simplify, distribute a to 8 and to 7.**
**False.** The correct operation is to distribute 8 to \(a\) and to 7, not the other way around.
2. **8(a) can be rewritten as 8a.**
**True.** This is correct as multiplication can be represented in this way.
3. **8(a + 7) can be rewritten as 8(a) + 8(7).**
**True.** This is a statement of the distributive property: \(8(a + 7) = 8a + 8 \times 7\).
4. **8(a + 7) can be rewritten as 8(a) + (7).**
**False.** This is incorrect; it would not respect the distributive property as it fails to multiply 7 by 8.
5. **An equivalent expression is 15a.**
**False.** The expression \(8(a + 7)\) does not simplify to \(15a\).
6. **An equivalent expression is 8a + 7.**
**False.** The correct expansion provides a term involving the multiplication of 8 by 7.
7. **An equivalent expression is 8a + 56.**
**True.** The correct expanded form is \(8a + 56\) after calculating \(8 \times 7 = 56\).
In summary, the true statements are:
- 8(a) can be rewritten as 8a.
- 8(a + 7) can be rewritten as 8(a) + 8(7).
- An equivalent expression is 8a + 56.
1. **To simplify, distribute a to 8 and to 7.**
**False.** The correct operation is to distribute 8 to \(a\) and to 7, not the other way around.
2. **8(a) can be rewritten as 8a.**
**True.** This is correct as multiplication can be represented in this way.
3. **8(a + 7) can be rewritten as 8(a) + 8(7).**
**True.** This is a statement of the distributive property: \(8(a + 7) = 8a + 8 \times 7\).
4. **8(a + 7) can be rewritten as 8(a) + (7).**
**False.** This is incorrect; it would not respect the distributive property as it fails to multiply 7 by 8.
5. **An equivalent expression is 15a.**
**False.** The expression \(8(a + 7)\) does not simplify to \(15a\).
6. **An equivalent expression is 8a + 7.**
**False.** The correct expansion provides a term involving the multiplication of 8 by 7.
7. **An equivalent expression is 8a + 56.**
**True.** The correct expanded form is \(8a + 56\) after calculating \(8 \times 7 = 56\).
In summary, the true statements are:
- 8(a) can be rewritten as 8a.
- 8(a + 7) can be rewritten as 8(a) + 8(7).
- An equivalent expression is 8a + 56.