Question

mary tried to evaluate an expression. here is her work: (3 + 7·3) - 3² + 2² = (10·3) - 3² + 2² step 1 = 30 - 3² + 2² step 2 = 30 - 9 + 4 step 3 = 21 + 4 step 4 = 25 step 5 is marys work correct? no, mary made a mistake going from the given expression to step 1. mary should have multiplied 7 and 3 before adding. the order of operations says to multiply before you add. no, mary made a mistake going from step 2 to step 3. mary should have added 3 and 2 instead of evaluating the exponents. the order of operations says to add before you evaluate exponents. yes, marys work is correct.

Explanation:

Step1: Analyze order of operations

According to PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), in the expression $(3 + 7\cdot3)-3^{2}+2^{2}$, we first calculate the multiplication inside the parentheses. So $7\cdot3 = 21$, and the expression becomes $(3 + 21)-3^{2}+2^{2}$. But Mary added 3 and 7 first in Step 1 which is wrong.

Step2: Correct calculation

$(3 + 7\cdot3)-3^{2}+2^{2}=(3 + 21)-9 + 4=24-9 + 4=15 + 4=19$.

Answer:

No, Mary made a mistake going from the given expression to Step 1. Mary should have multiplied 7 and 3 before adding. The order of operations says to multiply before you add.