Dondo76idn
Answered

Explore a diverse range of topics and get expert answers on IDNLearn.com. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.

Which of the following demonstrates the distributive property?

A. [tex]\((r + s)t = rt + st\)[/tex]
B. [tex]\((r + s)t = (s + r)t\)[/tex]
C. [tex]\((r + s)t = r + (st)\)[/tex]
D. [tex]\((r + s)t = t(r + s)\)[/tex]

Sagot :

GinnyAnsweridn
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]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.