Sure! Let's go through each of the given options to see which one demonstrates the distributive property.
The distributive property in mathematics states that for any numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[ a(b + c) = ab + ac \][/tex]
We'll compare each option to this form.
### Option A: [tex]\((r+s) t = r t + s t\)[/tex]
Using the distributive property:
[tex]\[ (r + s)t = rt + st \][/tex]
This matches the form of the distributive property.
### Option B: [tex]\((r+s) t = (s+r) t\)[/tex]
This option is actually demonstrating the commutative property of addition, not the distributive property:
[tex]\[ (r + s) = (s + r) \][/tex]
Multiplying both sides by [tex]\(t\)[/tex] gives:
[tex]\[ (r + s)t = (s + r)t \][/tex]
### Option C: [tex]\((r+s) t = r + (s t)\)[/tex]
This does not match the distributive property form:
[tex]\[ (r + s)t \neq r + (st) \][/tex]
Instead, it should be:
[tex]\[ (r + s)t = rt + st \][/tex]
### Option D: [tex]\((r+s) t = t(r+s)\)[/tex]
This option is demonstrating the commutative property of multiplication:
[tex]\[ t(r + s) = (r + s)t \][/tex]
The choice that demonstrates the distributive property is:
### Answer:
A. [tex]\((r+s) t = r t + s t\)[/tex]
