Which of the following is equivalent to multiplying [tex]$35 \times 21$[/tex]?

Select all that apply.

A. [tex] (7 \times 5) \times (7 \times 3) [/tex]

B. [tex] (30 \times 21) + (5 \times 21) [/tex]

C. [tex] 7(5 \times 3) [/tex] [tex] 7(5+3) [/tex]



Answer :

To determine which expressions are equivalent to multiplying 35 by 21, let’s analyze each option step-by-step.

### Option A: [tex]\((7 \times 5) \times (7 \times 3)\)[/tex]

First, evaluate the individual multiplications within the parentheses:
[tex]\[ 7 \times 5 = 35 \][/tex]
[tex]\[ 7 \times 3 = 21 \][/tex]

Now, multiply the results:
[tex]\[ 35 \times 21 \][/tex]

Since the original expression is [tex]\(35 \times 21\)[/tex], this option is equivalent.

### Option B: [tex]\((30 \times 21) + (5 \times 21)\)[/tex]

Here, let's use the distributive property to verify:
[tex]\[ (30 + 5) \times 21 \][/tex]

First, evaluate the sum:
[tex]\[ 30 + 5 = 35 \][/tex]

Then multiply:
[tex]\[ 35 \times 21 \][/tex]

This matches the original expression, so this option is equivalent.

### Option C: [tex]\(7(5 \times 3) 7(5 + 3)\)[/tex]

Let's break this down step-by-step:

1. Evaluate the expression inside the first set of parentheses:
[tex]\[ 5 \times 3 = 15 \][/tex]

2. Multiply by 7:
[tex]\[ 7 \times 15 \][/tex]

Moving to the next part of the expression:
1. Evaluate the expression inside the second set of parentheses:
[tex]\[ 5 + 3 = 8 \][/tex]

2. Multiply by 7:
[tex]\[ 7 \times 8 = 56 \][/tex]

The rewritten expression suggests comparing [tex]\(7 \times 15\)[/tex] with [tex]\(56\)[/tex]. Since neither of these products equal [tex]\(35 \times 21\)[/tex], option C is not equivalent.

### Conclusion:

The expressions that are equivalent to multiplying 35 by 21 are:

- Option A [tex]\((7 \times 5) \times (7 \times 3)\)[/tex]
- Option B [tex]\((30 \times 21) + (5 \times 21)\)[/tex]

So, the correct answers are:

- A
- B