To determine which of the given expressions has a value of 0 when [tex]\( a = 0 \)[/tex], let's evaluate each one step by step.
### Expression A
[tex]\[ a \cdot (1 - 3 + 2) \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ 1 - 3 = -2 \][/tex]
[tex]\[ -2 + 2 = 0 \][/tex]
Now multiply by [tex]\( a \)[/tex]:
[tex]\[ 0 \cdot 0 = 0 \][/tex]
So, expression A has a value of 0.
### Expression B
[tex]\[ (a + 2) \cdot (4 - 3) \][/tex]
First, evaluate the expressions inside the parentheses:
[tex]\[ a + 2 = 0 + 2 = 2 \][/tex]
[tex]\[ 4 - 3 = 1 \][/tex]
Now multiply the results:
[tex]\[ 2 \cdot 1 = 2 \][/tex]
So, expression B does not have a value of 0.
### Expression C
[tex]\[ a + (2 \cdot 3 + 4) \][/tex]
First, evaluate the multiplication and addition inside the parentheses:
[tex]\[ 2 \cdot 3 = 6 \][/tex]
[tex]\[ 6 + 4 = 10 \][/tex]
Now add [tex]\( a \)[/tex] to the result:
[tex]\[ 0 + 10 = 10 \][/tex]
So, expression C does not have a value of 0.
### Expression D
[tex]\[ (a - 4) \cdot 3 + 2 \][/tex]
First, evaluate the expression inside the parentheses and perform the multiplication:
[tex]\[ a - 4 = 0 - 4 = -4 \][/tex]
[tex]\[ -4 \cdot 3 = -12 \][/tex]
Now add 2 to the result:
[tex]\[ -12 + 2 = -10 \][/tex]
So, expression D does not have a value of 0.
### Conclusion
Out of all the expressions, only expression A has a value of 0 when [tex]\( a = 0 \)[/tex].
So, the correct answer is that expression A has a value of 0 when [tex]\( a = 0 \)[/tex].
