To determine which of the expressions are equivalent to [tex]\(10 \cdot (3+4)\)[/tex], we need to simplify and compare each expression step-by-step.
Given expression:
[tex]\[ 10 \cdot (3+4) \][/tex]
First, simplify the given expression:
[tex]\[ 10 \cdot (3+4) = 10 \cdot 7 = 70 \][/tex]
Next, we will check each of the given expressions:
Expression A: [tex]\(10 \cdot (4+3)\)[/tex]
Simplify the expression:
[tex]\[ 10 \cdot (4+3) = 10 \cdot 7 = 70 \][/tex]
This expression is equivalent to the given expression.
Expression B: [tex]\((3+4) \cdot 10\)[/tex]
Simplify the expression:
[tex]\[ (3+4) \cdot 10 = 7 \cdot 10 = 70 \][/tex]
This expression is also equivalent to the given expression.
Expression C: [tex]\((10 \cdot 3) + 4\)[/tex]
Simplify the expression:
[tex]\[ (10 \cdot 3) + 4 = 30 + 4 = 34 \][/tex]
This expression is not equivalent to the given expression.
Expression D: [tex]\(10 \cdot 3 + 10 \cdot 4\)[/tex]
Simplify the expression using the distributive property:
[tex]\[ 10 \cdot 3 + 10 \cdot 4 = 30 + 40 = 70 \][/tex]
This expression is equivalent to the given expression.
Summarizing these results, the expressions that are equivalent to [tex]\(10 \cdot (3+4)\)[/tex] are:
- Expression A: [tex]\(10 \cdot (4+3)\)[/tex]
- Expression B: [tex]\((3+4) \cdot 10\)[/tex]
- Expression D: [tex]\(10 \cdot 3 + 10 \cdot 4\)[/tex]
Therefore, the correct answers are:
- A. [tex]\(10 \cdot (4+3)\)[/tex]
- B. [tex]\((3+4) \cdot 10\)[/tex]
- D. [tex]\(10 \cdot 3 + 10 \cdot 4\)[/tex]
