1

Problem

Simplify the expression
\$ 3^2 \times (4 + 7)-(5 \times 2)^2 \div 2 \times (3 + 1) \$

2

Step

Given expression

\$ 3^2 \times (4+7)-(5 \times 2)^2 \div 2 \times (3+1) \$

3

Hint

To evaluate the expression, let’s follow the PEMDAS rule:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

4

Step

Evaluate expressions inside parentheses

4 + 7 = 11

\$5 \times 2\$ = 10

3 + 1 = 4

5

Step

Rewrite the expression with the evaluated values

\$ 3^2 \times (11)-(10)^2 \div 2 \times (4) \$

6

Step

Evaluate exponents

\$ 3^2 \$ = 9

\$ 10^2 \$ =100

7

Step

Rewrite the expression with the evaluated exponents

\$ 9 \times 11 - 100 \div 2 \times 4 \$

8

Step

Perform multiplication

\$ 9 \times 11 = 99\$

9

Step

Rewrite the expression with the evaluated multiplication

\$ 99 - 100 \div 2 \times 4 \$

10

Step

Perform division

\$ 100 \div 2 \$ = 50

\$ 99 - 50 \times 4 \$

11

Step

Perform multiplication

\$ 50 \times 4 \$ = 200

\$ 99 - 200 \$

12

Step

Perform subtraction

99 - 200 = -101

13

Solution

So, the final value of the expression is -101.

14

Sumup

Please Summarize Problem, Hint, Clue, Formula and Steps

Choices

15

Choice-A

The step is wrong; using the PEMDAS rule yields -101, not 99, as the result, contradicting the expected outcome

Wrong 99

16

Choice-B

The choice is incorrect because using the PEMDAS rule yields -101 instead of - 99 as the result

Wrong -99

17

Choice-C

The response is inaccurate because the application of the PEMDAS rule yields a result of -101, not 101

Wrong 101

18

Choice-D

This option is correct because by applying the PEMDAS rule we got the result as -101

Correct -101

19

Answer

Option

D

20

Sumup

Please Summarize Choices