Let's determine which of the given expressions is equivalent to the original expression [tex]\((3 \times p) - 6\)[/tex].
Given expression:
[tex]\[ (3 \times p) - 6 \][/tex]
Option A:
[tex]\[ (3 \times p) - 6 \][/tex]
This option exactly matches the given expression, so it is equivalent to the original expression.
Option B:
[tex]\[ (3 \times p) - (3 \times 6) \][/tex]
Simplify this expression:
[tex]\[ (3 \times p) - 18 \][/tex]
This is not equivalent to the original expression [tex]\((3 \times p) - 6\)[/tex].
Option C:
[tex]\[ (3 + p) - (3 + 6) \][/tex]
Simplify this expression:
[tex]\[ 3 + p - 9 \][/tex]
Combine like terms:
[tex]\[ p - 6 \][/tex]
This expression simplifies to [tex]\(p - 6\)[/tex], which is not equivalent to the given expression [tex]\((3 \times p) - 6\)[/tex].
Option D:
[tex]\[ (3 \times p) \times (3 \times 6) \][/tex]
Simplify this expression:
[tex]\[ 3p \times 18 \][/tex]
[tex]\[ 54p \][/tex]
This expression simplifies to [tex]\(54p\)[/tex], which is not equivalent to the given expression [tex]\((3 \times p) - 6\)[/tex].
Given these evaluations:
- Option A is equivalent to the original expression [tex]\((3 \times p) - 6\)[/tex].
- Options B, C, and D are not equivalent to the original expression.
Thus, the correct answer is:
Option A: [tex]\((3 \times p) - 6\)[/tex]
