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

Given expression

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

To simplify the expression, let’s follow the PEMDAS rule

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

Evaluate expressions inside parentheses

4 + 7 = 11

\$5 \times 2\$ = 10

3 + 1 = 4

Rewrite the expression with the evaluated values

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

Evaluate exponents

\$ 3^2 \$ = 9

\$ 10^2 \$ =100

Rewrite the expression with the evaluated exponents

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

Perform division

\$ 100 \div 2 \$ = 50

Rewrite the expression with the evaluated division

\$ 9 \times 11 - 50 \times 4 \$

Perform multiplication

\$ 9 \times 11 = 99\$

\$ 50 \times 4 = 200\$

Perform subtraction

99 - 200 = - 101

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

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

99

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

-99

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

101

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

-101

Option

D

Can you summarize what you’ve understood in the above steps?