Dondo76idn
Answered

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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]
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